Numerical Simulation of the Relaxation Behavior of Failed Sandstone Specimens
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Numerical Simulation of the Relaxation Behavior of Failed Sandstone Specimens Yuting Xue 1 & Brijes Mishra 2 Received: 14 April 2020 / Accepted: 11 June 2020 # Society for Mining, Metallurgy & Exploration Inc. 2020
Abstract The relaxation test on sandstone specimens showed typical behavior in pre-failure region and stepwise behavior in the postfailure region. Overall, more significant stress relaxation occurred within the failed specimens than the intact ones. Numerical simulations were conducted with pre-defined failure plane and with Voronoi tessellation to visualize the relaxation behavior. The model with pre-defined failure plane showed the key role of failure plane and asperity in simulating the step-wise post-failure relaxation behavior. The inhomogeneous stress distribution within failed specimen and the viscous deformation of intact rocks induced high stress concentration at the asperities. The observed step-wise relaxation initiated from the failure of asperity. Furthermore, the simulations with Voronoi tessellation showed time-dependent fracture development during relaxation in post-failure region. The presence of fractures completely changed the stress distribution. Stress concentration occurred at the front area of fractures and at the interacting areas between fractures. During relaxation, fractures still developed with time and the sudden significant increase in the “damage” coincided with the acceleration of stress relaxation leading to step-wise relaxation. Finally, the results showed the possibility of using residual strength as the long-term strength of failed rock. Keywords Sandstone . Relaxation . UDEC . Fracture development . Post-failure
1 Introduction The viscous behavior of coal measure rocks is of great importance for the time-dependent stability of underground coal structures. Mine roadways and pillars are these kinds of structures. They need to be maintained for decades, and their timedependent stability is the key for safe and efficient mining. The underground structures may experience various timedependent behaviors. The time-dependent behavior of a mine roof is normally demonstrated by a convergence curve [1]. The time-dependent roof convergence curve shows similar behavior as the creep curve with three stages. Convergence rate decreases rapidly at first, then remains constant, and finally accelerates to failure when the deformation exceeds a certain threshold value. Roof instability is identified from the accelerating convergence in the third stage. However, the roof convergence is not merely the result of the creep of intact * Brijes Mishra [email protected] 1
National Institute of Occupational Safety and Health, Pittsburgh, PA, USA
2
West Virginia University, Morgantown, WV, USA
rock. The viscosity values calculated from the measured convergence data are much smaller than those determined from laboratory test on intact specimens [2, 3]. The results indicate that, in addition to the creep of intact rock, other factors contribute to the time-dependent deformation, such
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