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Master’s & Doctoral Defenses

upcoming defensesThe Public presentation portion of a defense is open to everyone and is an especially valuable opportunity for graduate students to experience the process firsthand.

Note: All information is provided by the academic units.

James Ford

Title: Joint Inversion of Compact Operators
Program: Master of Science in Mathematics
Advisor: Dr. Jodi Mead, Mathematics
Committee: Dr. John Bradford, Geosciences and Dr. Grady Wright, Mathematics
Date: May, 24, 2017
Time: 9:00 p.m.
Location: Mathematics Building, Room 135

Read James Ford's Abstract Here

The first mention of joint inversion came in [20], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends using the singular value decomposi- tion to determine the conditioning of discrete joint inversion using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.
The operators are based on combining Green’s function solutions to differential equations representing different types of data. Joint operators are formed by extend- ing the concept of stacking matrices to one of combining operators. We propose that the effectiveness of joint inversion can be evaluated by comparing the decay rate of the singular values of the joint operator to those from the individual operators. The joint singular values are approximated by an extension of the Galerkin method given in [7, 16]. The approach is illustrated on a one-dimensional ordinary differential equation where slight improvement is observed when naively combining differential equations. Since this approach relies primarily on the differential equations representing data, it provides a mathematical framework for determining the effectiveness of joint inversion methods. It can be extended to more realistic differential equations in order to better inform the design of field experiments.

S M Naziur Mahmud

Title: Effect of Particle Size Distribution and Packing Characteristics on Railroad Ballast Shear Strength: A Numerical Study Using the Discrete Element Method
Program: Master of Science in Civil Engineering
Advisor: Dr. Debakanta Mishra, Civil Engineering
Committee: Dr. Arvin Farid, Civil Engineering and Dr. Bhaskar Chittoori, Civil Engineering
Date: May 25, 2017
Time: 12:00 p.m.
Location:  Environmental Research Building – Room 1127

Read S M Naziur Mahmud's Abstract Here

Railroad infrastructure plays a significant role in sustaining the economy of a country, and facilitates fast, safe and reliable transportation of passengers as well as commodities. Significant capital investments are required for the construction and maintenance of a railroad network that is structurally and functionally adequate. The ballast layer is one of the main structural components of a conventional rail track system, and comprises coarse-grained unbound particles, often as large as 63 mm in size. The ballast as a load bearing layer resists train-induced stresses through particle-particle interaction. Accordingly, particle size distribution and packing characteristics are important factors that govern the mechanical behavior of the ballast layer under loading. A well-performing ballast layer should ideally possess optimum drainage characteristics to ensure rapid removal of surface water, and adequate shear strength to restrain the track against excessive movement under loading. In-depth understanding of different factors affecting ballast behavior can help reduce recurrent costs associated with ballast maintenance.

Conducting commonly used shear strength tests on coarse-grained railroad ballast and performing parametric studies to quantify the effects of different material, specimen and test parameters on ballast shear strength is often not feasible in standard geotechnical engineering laboratories due to the significantly large specimen and test set-up requirements. In such situations, the Discrete Element Method (DEM) that facilitates micromechanical analysis of particulate system behavior becomes a logical alternative. The primary objective of this research effort was to study the effects of particle size distribution and packing characteristics on the shear strength behavior of railroad ballast. This was accomplished by simulating commonly used laboratory shear strength tests such as Direct Shear Test and Triaxial Monotonic Shear Strength Test using DEM. A commercially available three-dimensional DEM package (PFC3D®) was used for this purpose. Published laboratory test data was used to calibrate the numerical models. A series of parametric analyses were subsequently carried out to quantify the individual effects of different variables being studied on ballast shear strength behavior. In an effort to increase ballast shear strength through better packing within the granular matrix, a new gradation parameter, termed as the “Coarse-to-Fine (C/F) Ratio” was proposed. By changing the “coarse” and “fine” fractions within a particular gradation specification, the resulting effect on ballast shear strength was studied. Besides studying the particle to particle interaction within the ballast matrix, this study also focused on studying the phenomenon of geogrid-ballast interaction under different packing conditions. A recently developed parameter known as the “Geogrid Gain Factor” was used to quantify the benefits of geogrid reinforcement of ballast. The ultimate objective was to further the understanding of ballast behavior under loading, which will lead to better-performing railroad tracks.