Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mining Engineering

Committee Chair

Brijes Mishra

Committee Co-Chair

Keith Heasley

Committee Member

Keith Heasley

Committee Member

Yi Luo

Committee Member

Bruce Kang

Committee Member

G.S. Esterhuizen


In underground coal mines, roof falls are a major contributor to injuries and fatalities. Studies have related the occurrence of roof fall to weak immediate roof, high horizontal stress, entry orientation, etc. An often-neglected factor in studies on this topic has been the influence of time-dependent behavior of the roof rock on roof falls. The time-dependent roof failure activity involves both intact and failed rocks. Numerical simulation techniques are available that include time-dependent behavior; however, they lack constitutive models that consider both the intact and the failed behavior of rock. In addition, input properties for the creep models only include the intact rock properties that are determined through constant load (time-dependent) tests. For failed rock, standard creep tests cannot be performed on the rock specimens. This thesis aims to understand this behavior through the following steps:

 Develop a new laboratory test method

 Develop a new constitutive model that incorporates the pre- and post-failure behavior

 Implement the constitutive model into 3DEC

 Analyze the hypothetical mine geometry using the new constitutive model

First, this study develops a new relaxation equation based on Burgers Model. Relaxation tests studied rock specimens in both intact and failed stages. The results from the tests showed significant difference in the viscous property between intact and failed rocks. The results of these relaxation tests determined the viscous parameters with the new relaxation equation. Next, this study constructed numerical models of laboratory sized specimens in 3DEC software. The models incorporated the new relaxation equation, and model runs showed that stress relaxation is significantly present in the post-failure region, rather than in the pre-failure region. Further, a single entry mine model in 3DEC analyzed the influence of strength degradation and the variation in the viscous property on the time-dependent failure process. Variation in the viscous parameter showed significant effects on the failure process in the rock mass. A series of unconfined relaxation tests was performed on sandstone specimens and coal measure rocks. For sandstone, specimens were cored from sandstone blocks; for coal measure rocks, which include shale, sandy shale, and shaly limestone, cores were obtained from mine sites. The test results show that the relaxation behaviors of intact and failed rock specimens are different. The stress relaxation curves in the pre-failure region showed a typical, smooth stress relaxation behavior, while the stress relaxation demonstrates stepped behavior in the post-failure region. For coal measure rocks, the variation in the time-dependent properties of failed rock were insignificant. A viscoelastic-strain-softening constitutive model was developed by incorporating both time-dependent and strain-softening behavior. The model was included in the 3DEC software as a user-defined model. Parametric model runs based on the time-dependent laboratory tests verified the accuracy of the proposed model. Finally, the user-defined model, using hypothetical condition, investigated the influence of various factors on the time-dependent deformation and failure of massive and bedded roof. These simulations investigated the influence of directional horizontal stress, step-wise excavation, and bedding planes on the time-dependent response of mine roof. This research achieved a comprehensive understanding of the time-dependent formation of roof fall.