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<p>A time-dependent Hoek–Brown strain-softening constitutive model has been developed to simulate the behavior of underground coal-roof rock masses. This model accounts for strain-softening, where key strength parameters (m and s) decrease exponentially with plastic strain, transitioning from peak to residual strength. Keeping this in mind, a mathematical exponential expression has been developed to estimate the peak strength parameter with time. The constitutive model has two sets of strength parameters, i.e., peak strength parameters (<i>m</i><sub><i>rm</i></sub> and <i>s</i><sub><i>rm</i></sub>), and residual parameters (<i>m</i><sub><i>rmt</i></sub> and <i>s</i><sub><i>rmt</i></sub>). Due to the impracticality of lab testing large-scale coal masses, this study utilizes back analysis of 12 field cases—including immediate failed, stable, and long-term stable conditions—to estimate rock strength parameters. Numerical models of underground coal galleries were developed, incorporating real-world material properties, in-situ stress conditions, and a mesh size of 0.4&#xa0;m × 0.4&#xa0;m × 0.4&#xa0;m. A time-dependent strain-softening Hoek–Brown model was integrated into the simulations, capturing creep and the gradual reduction of rock strength over time. The model uses an elastic–plastic-strain softening model and introduces a peak reduction parameter to simulate time-sensitive weakening. This novel approach offers a practical alternative for deducing strength parameters in Indian coalfields. The efficiency of the models was analysed based on the mean absolute error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). The insights gained improve the understanding of long-term rock mass behavior and support the development of better mine design strategies, particularly for roof stability and collapse prevention in underground coal mining.</p>

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Assessment of Coal Roof Strength Degradation Using a Time-Dependent Strain-Softening Model

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Sonu Saran,
  • Prudhvi Raju Gadepaka,
  • Ashok Jaiswal

摘要

A time-dependent Hoek–Brown strain-softening constitutive model has been developed to simulate the behavior of underground coal-roof rock masses. This model accounts for strain-softening, where key strength parameters (m and s) decrease exponentially with plastic strain, transitioning from peak to residual strength. Keeping this in mind, a mathematical exponential expression has been developed to estimate the peak strength parameter with time. The constitutive model has two sets of strength parameters, i.e., peak strength parameters (mrm and srm), and residual parameters (mrmt and srmt). Due to the impracticality of lab testing large-scale coal masses, this study utilizes back analysis of 12 field cases—including immediate failed, stable, and long-term stable conditions—to estimate rock strength parameters. Numerical models of underground coal galleries were developed, incorporating real-world material properties, in-situ stress conditions, and a mesh size of 0.4 m × 0.4 m × 0.4 m. A time-dependent strain-softening Hoek–Brown model was integrated into the simulations, capturing creep and the gradual reduction of rock strength over time. The model uses an elastic–plastic-strain softening model and introduces a peak reduction parameter to simulate time-sensitive weakening. This novel approach offers a practical alternative for deducing strength parameters in Indian coalfields. The efficiency of the models was analysed based on the mean absolute error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). The insights gained improve the understanding of long-term rock mass behavior and support the development of better mine design strategies, particularly for roof stability and collapse prevention in underground coal mining.