Time-Dependent Rock Failure at Kartchner Caverns, Arizona

Assessing long-term rock stability is an important aspect in the analysis of slopes, dam and bridge foundations, and other infrastructure. Rock behavior over tens to thousands of years must be anticipated when predicting the performance of, for example, an underground containment facility for nuclear waste. At such long time scales, the time dependence of rock failure, typically ignored in short time scale analyses, has a significant effect and must be included in the analysis. Since time-dependent rock behavior is thought to be caused by the subcritical growth of microcracks, a time-dependent analysis should incorporate a method of simulating subcritical crack growth. In this thesis, a rock bridge damage model was developed using the finite element program Abaqus to simulate subcritical crack growth for all three modes of crack tip displacement in three-dimensional rock masses. Since subcritical crack growth is not among the damage initiation and evolution criteria available in Abaqus, its effect was included in the model through the USDFLD user subroutine. Material properties for the damage model were obtained through laboratory fracture toughness testing of Escabrosa limestone from Kartchner Caverns. Tests included the grooved disk test for mode I, the punch-through shear with confining pressure test for mode II, and the circumferentially-notched cylindrical specimen test for mode III. The subcritical crack growth parameters n and A were calculated for all three modes using the constant stress-rate method. Fracture test results were compared with a previous study by Tae Young Ko at the University of Arizona, which tested Coconino sandstone and determined that the subcritical crack growth parameters were consistent among modes. This thesis expands upon Ko's work by adding the characterization of a second rock material in all three modes; results indicate that for Escabrosa limestone the subcritical crack growth parameters are not consistent among modes. Additionally, the Escabrosa limestone composing the caverns ranges from a more homogeneous, even-grained texture to a more heterogeneous texture consisting of coarse-grained veins and solution cavities set in a fine-grained matrix. To determine if the veined regions are more susceptible to fracturing and act as the nuclei of rock bridge failure, the fracture toughness tests were conducted separately for each texture. Results indicate that the more heterogeneous limestone has a higher fracture strength, fracture toughness, and subcritical crack growth index n than the more homogeneous limestone. This is in agreement with previous studies that determined that a more complex and heterogeneous microstructure produces a larger microcrack process zone and a more tortuous crack path, leading to higher fracture energies and larger values of n. Application of the rock bridge damage model to a simplified Kartchner cave room with a single roof block provided visualization of decreasing rock bridge size and produced time-to-failure estimates of 1,251 to 65,850 years. Multiple models were run to study the effect of (i) using material properties from each of the two textures identified in the Escabrosa limestone and (ii) varying the in-situ stress ratio, K. Both the value of K and the choice of Escabrosa texture had a large effect on the estimated time-to-failure, indicating that for future modeling of Kartchner accurate estimation of the in-situ stress ratio is as important as field identification of homogeneous vs. heterogeneous textures