A Viscoelastic-Plastic Creep Model for Initial Damaged Coal Sample Affected by Loading Rate

Underground engineering rock masses are significantly affected by stress redistribution induced by mining or adjacent engineering disturbances, leading to initial damage accumulation in coal-rock masses. Under sustained geostress, these masses exhibit pronounced time-dependent creep behavior, posing serious threats to long-term engineering stability. Dynamic loading effects triggered by adjacent mining activities (manifested as medium strain-rate loading) further exacerbate damage evolution and significantly influence creep characteristics. In this study, coal samples with identical initial damage were prepared, and graded loading creep tests were conducted at rates of 0.005 mm·s−1 (50 microstrains·s−1), 0.01 mm·s−1 (100 microstrains·s−1), 0.05 mm·s−1 (500 microstrains·s−1), and 0.1 mm·s−1 (1000 microstrains·s−1) to systematically analyze the coupled effects of loading rate on creep behavior. Experimental results demonstrate that increased loading rates markedly shorten creep duration, with damage rates during the acceleration phase showing nonlinear surges (e.g., abrupt instability at 0.1 mm·s−1 (1000 microstrains·s−1)). Based on experimental data, an integer-order viscoelastic-plastic creep model incorporating stress-dependent viscosity coefficients and damage correlation functions was developed, fully characterizing four behaviors stages: instantaneous deformation, deceleration, steady-state, and accelerated creep. Optimized via the Levenberg–Marquardt algorithm, the model achieved correlation coefficients exceeding 0.96, validating its accuracy. This model clarifies the impact mechanisms of loading rates on the long-term mechanical behavior of initially damaged coal samples, providing theoretical support for stability assessment and hazard prevention in underground engineering.