Modified Rheological Model for Deep-Buried Silty Mudstone and Support Time Analysis Application

The rheological properties of soft rocks should be considered in the long-term design and maintenance of deep-buried tunnels using uniaxial single-stage loading and graded incremental cyclic-loading methods. In this article, creep tests were performed on deep-buried silty mudstone from a specific water conveyance tunnel in China, with a buried depth in the range of 1650–2320 m and subjected to high in situ stress. The creep curves of silty mudstone under different loading stresses were obtained, showing evident rheological mechanical behavior under complicated external environmental conditions. Based on the classic Burgers rheological model, a new nonlinear creep model was established based on the creep properties of deep-buried silty mudstone in the project area. Typically, the designated rheological models for certain projects are unsuitable or inadequate. A nonlinear dashpot was calculated using the Levenberg–Marquardt (L–M) method coupled with origin to account for the deterioration trend in the strength of the silty mudstone over time. With the determined parameters, the modified Burgers model exhibited good qualitative consistency with field monitoring data. The user-defined material mechanical behavior (UMAT) subroutine of the modified Burgers model was successfully achieved after it was implemented in the numerical code ABAQUS. Based on the full-rheological effect, the proper supporting time of a deep-buried tunnel was studied, and it was proposed that a second lining should be cast in situ approximately 150 days after the excavation of the tunnel. The outcomes of the proposed modified rheological model can accurately represent the creep behavior of deep-buried silty mudstones in a specific engineering instance. The research results can provide a basis for the rheological behavior and supporting time of deep-buried silty mudstone.