This dissertation provides a systematical investigation of computational approaches to mod- eling of granular materials. Granular materials are ubiquitous in everyday life and in a variety of engineering and industrial applications. Despite the apparent simplicity of the laws governing particle scale interactions, predicting the continuum mechanical response of granular materials still poses extraordinary challenges. This is largely due to the complex his- tory dependence resulting from continuous rearrangement of the microstructure of granular material, as well as the mechanical interlocking due to grain morphology and surface rough- ness. X-Ray Computed Tomography (XRCT) is used to characterize the grain morphology and the fabric of the granular media, naturally deposited sand in this study. The Level-Set based Discrete Element Method (LS-DEM) is then used to bridge the granular behavior gap between the micro and macro scale. The LS-DEM establishes a one-to-one correspondence between granular objects and numerical avatars and captures the details of grain morphology and surface roughness. However, the high fidelity representation significantly increases the demands on computational resources. Herein, we introduce an enhanced image processing workflow for XRCT images in order to optimize the grain and fabric resolution. A parallel version of LS-DEM is then introduced to significantly decrease the computational demands. The code employs a binning algorithm, which reduced the search complexity of contact de- tection from O(n2) to O(n), and a do- main decomposition strategy is used to elicit parallel computing in a memory- and communication- efficient manner. The parallel implementation shows good scalability and efficiency.

High fidelity LS avatars obtained from XRCT images of naturally deposited sand are then used to replicate the results of triaxial tests using the new parallel LS-DEM. Both micro- and macro-mechanical behaviors of natural materials were well captured and validated with experimental data. The results of the numerical modeling show that the primary source of peak strength of sand is the mechanical interlocking between irregularly shaped grains. Flexible membrane simulations with a rotatable loading platen were found to accurately match experimentally observed relationships between deviatoric stress and mobilized friction angle with axial shortening for naturally deposited sand. Finally, we investigated the viability of modeling dynamic problems with newly formulated impulse-based LS-DEM. The new formulation is stable, fast and energy conservative, however, it may be numerically stiff when the assembly has a substantial mass difference or badly reconstructed particles as a result of poor image resolution. We also demonstrated the feasibility of modeling deformable structures in the rigid body framework and proposed several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contact and dynamic collision. We also extended the impulse-based LS-DEM to include arbitrarily shaped topography surfaces and exploited algorithmic advantages to investigate interactions between topography and colliding objects. The novel formulation significantly improves performance and allows for larger timesteps, which is advantageous for observing the full development of physical phenomena such as rock avalanches.

Rock falls were monitored in Yosemite Valley using seismic and infrasound sensors in order to gain insights into the feasibility of rock fall detection and rock fall processes. The research objectives were to characterize the rock fall seismic signal and use that data to study the initiation, triggering, and dynamics of rock falls, correlate the data with physical and environmental conditions, and to search for potential rock fall precursors. Yosemite Valley has approximately one rock fall per week in an area that measures 15 km2, making it an ideal laboratory for monitoring rock falls. Data were collected continuously at 500-1000 sps using a network of one to four stations during two winter seasons. Three stations were located within a 600 m long footprint on the cliff or at the base of the historically active Middle Brother formation and one station was located 2 km to the east. There were three widely reported rock falls that were also easily identifiable in the seismic data: these three events were critical in the development of a triggering algorithm and criteria for distinguishing rock falls from the thousands of triggers. In addition to rock falls, snow avalanches, construction activity, rain, wind, pressure waves generated from Yosemite Falls, thermally-driven long period seismic anomalies, and earthquakes triggered or were identified in the seismic and acoustic data. A total of twelve to seventeen rock falls were recorded, out of which only eight were reported by eyewitnesses. All but one rock fall event came from within one kilometer of the seismic network and originated at four distinct source areas. The spectral similarities between some events allowed them to be placed with high certainty as coming from a particular talus slope even when there were too few stations in operation to precisely locate the source. Detachment and impact signals were recorded for multiple rock fall events, and timing delay between detachment and impact correlated well with physical parameters such as falling and impact distances. The Ahwiyah Point rock fall on 28 March 2009 was a large enough event to have been widely captured on regional seismic networks and is the only rock fall recorded at a distance greater than 1 km. The Ahwiyah Point rock fall was uniquely well-documented with pre and post rock fall high resolution photography and LiDAR to supplement the seismic and acoustic data. The rock fall dynamics were resolved by integrating these different data to show that a large block detached, slid off of a steeply dipping ledge, launched into a ballistic trajectory, impacted the cliff with enough force to detach another large volume of rock, continued down the cliff face to the talus, and produced an airblast upon impact. P and Rayleigh wave phases were recorded for multiple rock falls, although S-waves were generally not detected. P-waves were calculated to have arrived via granitic cliff faces rather than directly through unconsolidated valley sediments via single station polarities and multiple station timing delays. Rayleigh waves generated by rock falls on the same cliff as the seismic sensor travel along and are oriented to the cliff face (e.g. tilted from normal). However Rayleigh waves do appear to travel through the valley when arriving from other cliffs and can be difficult to identify due to boundary interactions at the base of the cliff. Distances were calculated using the phase arrival differences of P and Rayleigh waves and the arrival time differences of P and infrasound acoustic waves. Thus, rock falls were successfully detected, located, and their dynamics reconstructed with the seismic and acoustic data.