Asa calculation method based on the Galerkin variation, the numerical manifold method (NMM) adopts a double covering system, which can easily deal with discontinuous deformation problems and has a high calculation accuracy. Aiming at the thermo-mechanical (TM) coupling problem of fractured rock masses, this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the in fluence of temperature field, deduces related system equations, and proposes a penalty function method to deal with boundary conditions. Numerical examples are employed to con firm the effectiveness and high accuracy of this method. By the thermal stress analysis of a thick-walled cylinder (TWC), the simulation of cracking in the TWC under heating and cooling conditions, and the simulation of thermal cracking of the Swedish & Auml;sp & ouml; Pillar Stability Experiment (APSE) rock column, the thermal stress, and TM coupling are obtained. The numerical simulation results are in good agreement with the test data and other numerical results, thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Freeze-thaw failure of frozen rock slope often occurs during engineering construction and mining in cold area, which poses a great threat to engineering construction and people's life safety. The properties of rock mass in cold region will change with the periodic change of temperature, which makes it difficult to accurately evaluate the stability of slope under the action of freeze-thaw cycle by conventional methods. Based on field investigation and literature review, this paper discusses the characteristics of frozen rock mass and the failure mechanism of frozen rock slope, and gives the types and failure modes of frozen rock slope. Then, the research status of frozen rock slope is analyzed. It is pointed out that the failure of frozen rock slope is the result of thermo-hydro-mechanical (THM) coupling. It is considered that freeze-thaw cycle, rainfall infiltration and fracture propagation have significant effects on the stability of frozen rock slope, and numerical simulation is used to demonstrate. The research shows that the safety factor of frozen rock slope changes dynamically with the surface temperature, and the safety factor of slope decreases year by year with the increase of freeze-thaw cycles, and the fracture expansion will significantly reduce the safety factor. Based on the above knowledge, a time-varying evaluation method of frozen rock slope stability based on THM coupling theory is proposed. This paper can deepen scholars' understanding of rock fracture slope in cold area and promote related research work.