Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mining Engineering

Committee Chair

Brijes Mishra

Committee Member

Yi Luo

Committee Member

Felicia Peng

Committee Member

Ihsan B Tulu

Committee Member

Ming Gu


The heterogeneity in the rock formation affects both rock behavior and the strength. The effect of heterogeneity is observed both at the laboratory scale and at the rockmass level. The mechanical properties of intact rock vary considerably at laboratory scale and often an average value is used for design purposes. Similarly, the values are arbitrarily scaled when used at rockmass level. In underground coal mines, the effect of variability of properties is often observed with the erratic roof failure events that occur throughout the mine. The approach often was to use the deterministic values from limited site data to estimate the rock strength and ignoring the inherent variability of rockmass properties. However, current numerical models have successfully captured the global behavior showing the effect of in-situ stress, geology, operational parameters, etc. This dissertation proposes a probabilistic approach that assumes that rockmass properties as random variables and examines its effect on underground coal mine.

The effect of random properties was examined by comparing the deterministic and completely random models which showed the importance of using randomness factor in rocks. Subsequently a spatially correlated random model investigated the influence of rock heterogeneity on rock strength and failure propagation. A random field database with specific spatial correlation was created for each physico-mechanical property using laboratory data and Extreme Value stochastic model in MATLAB. Two scale-measured parameters defined the correlation length, which controls the spatially correlated random data. Then, to verify the importance of the four parameters, friction, cohesion, and correlation length along the horizontal and vertical axes, one hundred and fifty two random sample data are generated. The stress for each specimen is tracked at different loading steps with different spatial correlation factors. This approach determined the effect of material model parameters affect the internal stress distribution for intact rocks. The models were further validated by predicting the behavior of rocks from controlled triaxial tests. Results from the laboratory tests were matched the predicted behavior from numerical models verifying the proposed stochastic method.

The stochastic method was then implemented in the three-dimensional numerical model to investigate a longwall mine operating in Pittsburgh seam. The influence of random field data on entry roof in the longwall mining system was investigated. Based on Extreme Value stochastic model, the realistic random field database added two scale-measured parameters from both horizontal and vertical directions to control the spatial correlation length. This model also considered a number of cutting sequences, for identifying the effect of the spatial variance on the roof behavior. Finally, the outcome of the dissertation was to use probabilistic approach for demonstrating the heterogeneous characteristic of rock and the influence of spatial variance on the failure mechanism of both intact rock and rockmass.