Tackling Data-Limited Rock Mechanics Models

Rock mechanics models are "data-limited," i.e., one seldom knows enough about a rock mass to use computational models unambiguously. Statistical methods, however, are capable of being applied where there are good data but a limited understanding of certain natural phenomena, such as the creep of rock salt or coal burst mechanics. To demonstrate the use of statistical-analytical techniques in rock mechanics problems, two case studies are used. The first study involves a historic examination of a nuclear waste repository in rock salt, where mathematical models are built using excavation convergence data to identify significant variables and estimate future deformation and stability. The second case study focuses on ongoing analysis of coal burst mechanics and associated factors. Over the last three decades, a hybrid statistical-analytical methodology has been applied for identifying significant factors affecting coal burst. The final model utilizes data from 30 case studies from Utah, Colorado, Kentucky, and other Eastern U.S. mines providing predictive capability for the entire United States coal fields. 1. INTRODUCTION There are two methods used by engineers and researchers as tools to help predict conditions in the future: statistical and computational. Starfield and Cundall (1988) identify rock mechanics models as "data-limited," that is, one seldom knows enough about a rock mass to use computational models unambiguously. Statistical methods, on the other hand, are uniquely capable of being applied where there are good data but a limited understanding of certain natural phenomena, such as the creep of rock salt or elevated risk domains associated with the violent failure of strata commonly referred to as coal bumps or bursts. Rock bursts and coal bumps are defined as sudden, violent failure that occur near mine entries that are of such a magnitude that they expel large amount of rock and/or coal into an excavation, restricting safe and efficient access to the working area (Maleki and White 1997). Gradual failure and spalling is common in coal mine environment and is considered not problematic but controlled through proper mine orientation and application of support as needed. Important to these real-world statistical evaluations are (1) having sufficient number of data collected consistently and (2) incorporation of analytical calculations for quantifying geologic, mining and particularly geotechnical variables. By combining the strength of the statistical and analytical models, an improved "hybrid" model is created and utilized. Powerful examples of the use of statistical techniques to evaluate stability and performance using significant field investigations are given by Parson and Dahl (1971), Maleki and White (1997), Maleki and Owen (2001), Maleki et al. (2001), Maleki et al. (2023), and Maleki (2023).