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Skewed bridges have exhibited poorer performance during lateral earthquake loading when compared to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Results from small-scale laboratory tests by Rollins and Jessee (2012) and numerical modeling by Shamsabadi et al. (2006) suggest that skewed bridge abutments may provide only 35% of the non-skewed peak passive resistance when a bridge is skewed 45°. This reduction in peak passive force is of particular importance as 40% of the 600,000 bridges in the United States are skewed (Nichols 2012). Passive force-deflection results based on large-scale testing for this study largely confirm the significant reduction in peak passive resistance for abutments with longitudinal reinforced concrete wingwalls. Large-scale lateral load tests were performed on a non-skewed and 45° skewed abutment with densely compacted sand backfill. The 45° skewed abutment experienced a 54% reduction in peak passive resistance compared to the non-skewed abutment. The peak passive force for the 45° skewed abutment was estimated to occur at 5.0% of the backwall height compared to 2.2% of the backwall height for the non-skewed abutment. The 45° skewed abutment displayed evidence of rotation, primarily pushing the obtuse side of the abutment into the backfill, significantly more than the non-skewed abutment as it was loaded into the backfill. The structural and geotechnical response of the wingwalls was also monitored during large-scale testing. The wingwall on the obtuse side of the 45° skewed abutment experienced nearly 6 times the amount of horizontal soil pressure and 7 times the amount of bending moment compared to the non-skewed abutment. Pressure and bending moment distributions are provided along the height of the wingwall and indicate that the maximum moment occurs approximately 20 in (50.8 cm) below the top of the wingwall. A comparison of passive force per unit width suggests that MSE wall abutments provide 60% more passive resistance per unit width compared to reinforced concrete wingwall and unconfined abutment geometries at zero skew. These findings suggest that changes should be made to current codes and practices to properly account for skew angle in bridge design.

Passive force-deflection behavior for densely compacted backfills must be considered in bridge design to ensure adequate resistance to both seismic and thermally induced forces. Current codes and practices do not distinguish between skewed and non-skewed bridge abutment geometries; however, in recent years, numerical models and small-scale, plane-strain laboratory tests have suggested a significant reduction in passive force for skewed bridge abutments. Also, various case studies have suggested higher soil stresses might be experienced on the acute side of the skew angle. For these reasons, three large-scale tests were performed with abutment skew angles of 0, 15 and 30 degrees using an existing pile cap [11-ft (3.35-m) wide by 15-ft (4.57-m) long by 5.5-ft (1.68-m) high] and densely compacted sand backfill confined by MSE wingwalls. These tests showed a significant reduction in passive force (approximately 38% as a result of the 15 degree skew angle and 51% as a result of the 30° skew angle. The maximum passive force was achieved at a deflection of approximately 5% of the backwall height; however, a substantial loss in the rate of strength gain was observed at a deflection of approximately 3% of the backwall height for the 15° and 30° skew tests. Additionally, the soil stiffness appears to be largely unaffected by skew angle for small displacements. These results correlate very well with data available from numerical modeling and small-scale lab tests. Maximum vertical backfill displacement and maximum soil pressure measured normal to the skewed backwall face were located on the acute side of the skew for the 15° and 30° skew test. This observation appears to be consistent with observations made in various case studies for skewed bridge abutments. Also, the maximum outward displacement of the MSE wingwalls was located on the obtuse side of the skew. These findings suggest that changes should be made to current codes and practices to properly account for skew angle in bridge design.

Bridge abutments are designed to withstand lateral pressures from thermal expansion and seismic forces. Current design curves have been seen to dangerously over- and under-estimate the peak passive resistance and corresponding deflection of abutment backfills. Similar studies on passive pressure have shown that passive resistance changes with different types of constructed backfills. The effects of changing the length to width ratio, or including MSE wingwalls determine passive force-deflection relationships. The purpose of this study is to determine the effects of the wall heights and of the MSE support on passive pressure and backfill failure, and to compare the field results with various predictive methods. To compare the effects of backfill geometries, three large-scale tests with dense compact sand were performed with abutment backfill heights of 3 ft (0.91 m), 5.5 ft (1.68 m), and 5.5 ft (1.68 m) confined with MSE wingwalls. Using an existing pile cap 11 ft (3.35 m) wide and 5.5 ft (1.68 m) high, width to height ratios for the abutment backfills were 3.7 for the 3ft test, and 2.0 for the 5.5ft and MSE tests. The failure surface for the unconfined backfills exhibited a 3D geometry with failure surfaces extending beyond the edge of the cap, increasing the "effective width", and producing a failure "bulb". In contrast, the constraint provided by the MSE wingwalls produced a more 2D failure geometry. The "effective width" of the failure surface increased as the width to height ratio decreased. In terms of total passive force, the unconfined 5.5ft wall provided about 6% more resistance than the 5.5ft MSE wall. However, in terms of passive force/width the MSE wall provided about 70% more resistance than the unconfined wall, which is more consistent with a plane strain, or 2D, failure geometry. In comparison with predicted forces, the MSE curve never seemed to fit, while the 3ft and 5.5ft curves were better represented with different methods. Even with optimizing between both the unconfined curves, the predicted Log Spiral peak passive forces were most accurate, within 12% of the measured peak resistances. The components of passive force between the unconfined tests suggest the passive force is influenced more by frictional resistance and less by the cohesion as the height of the backwall increases.

Numerical Analysis of Passive Force on Skewed BridgeAbutments with Reinforced Concrete WingwallsScott Karl SnowDepartment of Civil and Environmental Engineering, BYU Master of Science Historically bridges with skewed abutments have proven more likely to fail during earthquake loadings (Toro et al, 2013) when compared to non-skewed bridges (Apirakvorapinit et al. 2012; Elnashai et al. 2010). Previous studies including small-scale laboratory tests by Jessee (2012), large-scale field tests by Smith (2014), and numerical modeling by Shamsabadi et al. (2006) have shown that 45° skewed bridge abutments experience a reduction in peak passive force by about 65%. With numerous skewed bridges in the United States, this study has great importance to the nation's infrastructure.The finite element models produced in this study model the large-scale field-testing performed by Smith (2014), which was performed to study the significant reduction in peak passive resistance for abutments with longitudinal reinforced concrete wingwalls. The finite element models largely confirm the findings of Smith (2014). Two models were created and designed to match the large-scale field tests and were used to calibrate the soil parameters for this study. Two additional models were then created by increasing the abutment widths from 11 feet to 38 feet to simulate a two-lane bridge. The 45° skewed 11-foot abutment experienced a 38% reduction in peak passive resistance compared to the non-skewed abutment. In contrast, the 45° skewed 38-foot abutment experienced a 65% reduction in peak passive resistance compared to the non-skewed abutment. When the wingwalls are extended 10 feet into the backfill the reduction decreased to 59% due to the change in effective skew angle.The finite element models generally confirmed the findings of Smith (2014). The results of the 11- and 38-foot abutment finite element models confirmed that the wingwall on the obtuse side of the 45° skewed abutments experienced approximately 4 to 5 times the amount of horizontal soil pressure and 5 times the amount of bending moment compared to the non-skewed abutment. Increases in the pressures and bending moments are likely caused by soil confined between the obtuse side of the abutment and the wingwall.A comparison of the 11- and 38-foot 45° skewed abutment models showed a decrease in the influence of the wingwalls as the abutment widened. The wingwall on the acute side of the 38-foot abutment developed approximately 50% of the horizontal soil pressure compared to the 11-foot abutment. The heave distribution of the 11-foot abutment showed approximately 1- to 2-inches of vertical displacement over a majority of the abutment backwall versus more than half of the 38-foot abutment producing ½ an inch or less.

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[pt] O estudo das propriedades estatísticas dos sistemas dinâmicos temsido uma área de pesquisa ativa nas últimas décadas. Seu principal objetivoé investigar quando determinados sistemas caóticos determinísticos exibemcomportamento estocástico quando examinados pelas lentes de uma medidainvariante relevante. Algumas das principais ferramentas empregadas naobtenção desses resultados são as propriedades espectrais do operador detransferência. No entanto, determinados sistemas do tipo produto torcido,incluindo cociclos lineares aleatórios e cociclos mistos aleatórios-quaseperiódicos, não se encaixam nessa abordagem. Trabalhos muito recentesobtiveram leis limite para esses sistemas estudando o operador de Markov.O objetivo desta dissertação é explicar como esses operadores podem serusados para derivar leis limite, como Estimativas de Grandes Desvios e oTeorema do Limite Central, para certos sistemas dinâmicos do tipo produtotorcido. / [en] The study of statistical properties of dynamical systems has been an active research area in recent decades. Its main goal is to investigate when certain deterministic chaotic systems exhibit stochastic behavior when examined through the lens of a relevant invariant measure. Some of the key tools employed in deriving such results are the spectral properties of the transfer operator. However, certain skew product systems, including random and mixed random-quasiperiodic linear cocycles, do not fit this approach. Very recent works have obtained limit laws for these systems by studying the Markov Operator. The purpose of this dissertation is to explain how these operators can be used to derive limit laws, such as Large Deviations Estimates and Central Limit Theorem, for certain skew-product dynamical systems.

Integrated systems with billions of transistors on a single chip are a now reality. These systems include multi-core microprocessors and are built today using deca-nanometer devices organized into synchronous digital circuits. The movement of data within such systems is regulated by a set of predictable timing signals, called clocks, which must be distributed to a large number of sequential elements. Collectively, these clocks have a significant impact on the frequency of operation and, consequently, on the performance of the systems. The clocks are also responsible for a large fraction of the power consumed by these systems. The objective of this dissertation is to better understand clock distribution in order to identify opportunities and strategies for improvement by analyzing the conditions under which the optimal tradeoff between power and performance can be achieved, by modeling the constraints associated with local and global clocking, by evaluating the impact of noise, and by investigating promising new design strategies for future integrated systems.