A general convolutional version of perfectly matched layer (PML) formulation for second-order wave equations with displacement as the only unknown based on the coordinate stretching is proposed in this study, which overcomes the limitation of classical PML in splitting the displacement field and requires only minor modifications to existing finite element programs. The first contribution concerns the development of a robust and efficient finite element program QUAD-CPML based on QUAD4M capable of simulating wave propagation in an unbounded domain. The more efficient hybrid-stress finite element was incorporated into the program to reduce the number of iterations for the equivalent linear dynamic analysis and the total time for the direct time integration. The incorporation of new element types was verified with the QUAD4M solutions to problems of dynamic soil response and the efficiency of hybrid-stress finite element was demonstrated compared to the classical finite elements. The second development involves the implementation of a general convolutional perfectly matched layer (CPML) as an absorbing boundary condition for the modeling of the radiation of wave energy in an unbounded domain. The proposed non-split CPML formulation is displacement-based, which shows great compatibility with the direct time integration. This CPML formulation treats the convolutional terms as external forces and includes an updating scheme to calculate the temporal convolution terms arising from the Fourier transform. In addition, the performance of the CPML has been examined by various problems including a parametric study on a number of key coefficients that control the absorbing ability of the CPML boundary. The final task of this thesis is to apply the developed CPML models to the dynamic analyses of soil-structure interaction (SSI) problems. Typical loading conditions including external load on the structure and underground wave excitation on the medium has been considered. Practical applications of CPML models include the numerical study on the effectiveness of the rubber-soil mixture (RSM) as an earthquake protection material and the report of vibrations induced by the passage of a high-speed train. The former investigates the effectiveness of the CPML models for the evaluation of the performance of RSM subject to seismic excitation and the latter tests the boundary effects on the accuracy of the results for train induced vibrations. Both studies show that CPML as an absorbing boundary condition is theoretically sound and effective for the analysis of soil-structure dynamic response. / published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

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This study addresses the influences on ridge basalt chemistry, through analysis of their major and trace element and isotopic composition at scales ranging from individual ridge segments to the entire length of the ridge system. Local-scale studies of basalts along the Mid-Atlantic Ridge shed light on crustal accretion at slow-spreading ridges, and on the nature of plume-ridge interaction in this region. We show that segments must have multiple supplies of magma delivered along their length, but with preferential delivery of magma to segment centers. Plume-ridge interaction near the Azores is not simple two- component mixing between “plume” mantle and “depleted” mantle as previously argued. The elevated highly incompatible trace element ratios possessed by basalts well south of the plume are the definitive sign of a low-degree melt, which can fractionate highly incompatible element ratios. We show that a low-degree melt of plume mantle acts to metasomatize ambient depleted mantle, creating a mixed source that melts to produce the enriched basalts south of the Azores. This metasomatized source is the enriched mixing component that produces the observed geochemical gradient, rather than bulk plume mantle. The latter half of this study is global in scope, involving a carefully compiled ridge basalt geochemical database. This database is unparalleled in size and coverage – including data from portions of the Gakkel and Southwest Indian Ridges and Lau basin that were unavailable in prior data compilations. It includes a catalog of 771 global ridge segments, enabling the calculation of mean MORB by averaging the “segment means”, including weighting on segment length and spreading rate and a quantitative treatment of errors. We show that the mean composition of ocean ridge basalts is more enriched than previously suggested, and argue for a re-definition of “normal MORB”. Segment basalt compositions are individually corrected for crystal fractionation, arriving at parental magma compositions that can be interpreted in terms of mantle processes. The fractionation-corrected mean segment compositions correlate with ridge depth, and with each other, in a manner that is consistent with control by mantle temperature variations. Mantle compositional heterogeneity is also seen, but appears to be a second-order effect. / Earth and Planetary Sciences

published_or_final_version / abstract / toc / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Civil Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy