A New Strain-Softening Anisotropic Constitutive Model for Coal Mine Roof Simulation

Injuries and fatalities resulting from roof falls are still a major concern in U.S. coal mines, and many researchers are focused on developing meaningful approaches to minimize this hazard. In the United States, coal mine roofs can vary widely in composition, geometry, and inherent heterogeneity, leading to a wide array of different roof fall failure types. Researchers frequently employ numerical modeling tools to reproduce this physical phenomenon and provide key guides to engineers regarding roof conditions and control as long as the input data and constitutive relations are appropriately selected. Simulating such complexity requires expertise and constitutive models that adequately simulate roof behaviors. However, the currently available constitutive models have shortcomings in capturing some of the roof fall failure types common in underground coal mines, such as guttering. A new constitutive model is developed to address the shortcomings of constitutive models commonly used for coal roof stability analysis. The constitutive model developed in this study combines the anisotropic-elasticity and nonlinear strain-softening responses. In addition, the developed constitutive model can simulate up to three different joint sets implicitly, allowing for use in both continuum and discontinuum settings, and can be used in both Lagrangian finite-volume and distinct element method codes of Itasca. First, the mathematical expressions of the model are provided. Afterward, the validation phase of the developed model that covers comparisons with analytical solutions and those of existing models (e.g., anisotropic elasticity, ubiquitous-joint, and bilinear strain-hardening/softening ubiquitous-joint plasticity) is presented. Finally, a hypothetical coal mine roadway facing high horizontal stress is simulated. The presented model successfully shows three distinct stages of a cutter roof in a shale roof: (1) initiation of shear cracks at the rib– roof intersection, (2) extension of cracks deeper into the roof (i.e., above the roof bolt length horizon), and (3) cantilevered roof. It is demonstrated that the presented constitutive model has the potential to help future researchers in simulating various roof responses.