To study the long-term stability of geothermal tunnels within a laminated rock mass, creep tests were conducted on slate with different bedding angles under different temperatures. In this study, we investigated the creep rate and macroscopic failure characteristics of slate with various bedding angles (0–90°). The coupled damage was considered, and combining with the unsteady fractional order theory, a constitutive model that can describe nonlinear behavior of laminated slate under thermal loading was established. The results show that gradual increases in temperature from 20 to 150 °C and loading from 10 to 115 MPa lead to increased rock damage, which leads to accelerated creep and eventual failure of the rock. The long-term strengths of slate with a bedding angle of 0 °C at temperatures of 20, 50, 80, 110, and 150 °C were found to be 126.21, 118.25, 106.18, 94.58, and 85.14 MPa, respectively, and its mechanical properties exhibited anisotropy. The proposed creep model effectively captures the three-stage creep characteristics of high-temperature layered rocks. The results of this study provide theoretical guidance for the long-term stability assessment of geothermal drilling in surrounding rock.
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