In order to study the deterioration mechanism of the shear creep characteristics of the soft interlayer of Permian carbonaceous shale in southwest China by acidic environment, this study focuses on Permian carbonaceous mudstone shale as the research subject, employing both laboratory experiments and theoretical modeling. Field sampling and XRD mineral composition analysis (with calcite as the primary component at 69%) were conducted, we utilized the self-developed THMC-B multi-field coupled shear rheometer. Rock samples were immersed in oxalic acid solutions and distilled water at different pH values (1, 3, 5, 7, and natural state), followed by conventional shear tests and graded loading shear creep tests. These experiments simulated the chemical effects of in-situ wet-dry cycles to analyze the influence of acid erosion on creep deformation. The test results indicate that under the same normal stress, the stronger the environmental acidity (lower pH value), the smaller the shear stress required for carbonaceous mudstone to undergo creep failure, and the larger the instantaneous elastic deformation and creep deformation. At low normal stress (e.g., 0.2 MPa), weak interlayers are more sensitive to acid corrosion, and structural damage caused by acid corrosion dominates creep deformation. As acidity increases (pH ≤ 3), the failure mode transitions from brittle to ductile.. In this study, a factor (D) coupling chemical damage and stress damage is innovatively introduced, and a fractional Abel sticky pot is used to replace the traditional Newtonian body, and a damage constitutive model that can accurately describe the three-stage creep characteristics of the soft interlayer in acid etching environment is constructed. Using particle swarm optimization algorithms combined with experimental data for parameter inversion, the model"s correlation coefficient R2 exceeds 0.96, validating that the model effectively describes the transient, steady-state, and accelerated creep characteristics of weak interlayers in an acid-etching environment. The research findings provide a theoretical basis for long-term stability analysis for slopes containing weak interlayers in acidic environments.