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In deep geological repositories for spent fuel and high-level radioactive waste (SF/HLW), a great deal of gas will be produced by anaerobic corrosion of metals, radiolysis of water and microbial degradation of organic materials.Due to the extremely low permeability of saturated compacted bentonite, gas will accumulate in the space in the bentonite around the waste canister, resulting in generation of a high gas pressure nearby the waste canister.Migration of gas in the engineered barrier system can be divided into four phases according to the gas pressure level: advection and diffusion of dissolved gas, visco-capillary two-phase flow, dilatancy-controlled gas flow and gas flow along macroscopic tensile fractures.Based on the characteristics of gas flow (i.e., gas migrates along discretely distributed pathways and is influenced by the stress state) and the modified gas pressure dependent permeability method from literatures, a modified approach with consideration of stress state was established.With this modified approach, the calculated results were improved, while it cannot describe the discrete distribution of gas flow pathways.Therefore, further modification with consideration of heterogeneity was proposed.On the basis of the existing experimental results under different boundary conditions, verification and comparison of the evolutions of the gas fluxes and the degree of saturation were conducted.Results show that the proposed approach in this article can effectively simulate the performance of gas permeability and the evolution of the degree of saturation during the two-phase flow and the dilatancy-controlled flow phases.