SUMMARY
Considerable bridge‐ground interaction effects are involved in evaluating the consequences of liquefaction‐induced deformations. Due to seismic excitation, liquefied soil layers may result in substantial accumulated permanent deformation of sloping ground near the abutments. Ultimately, global response is dictated by the bridge‐ground interaction as an integral system. However, a holistic assessment of such response generally requires a highly demanding full three‐dimensional (3D) model of the bridge and surrounding ground. As such, in order to capture a number of the salient involved mechanisms, this study focuses on the longitudinal seismic performance of a simpler idealized configuration, motivated by details of an existing bridge‐ground configuration. In this model, a realistic multilayer soil profile is considered with interbedded liquefiable/nonliquefiable strata. The effect of the resulting liquefaction‐induced ground deformation is explored. Attention is given to overall deformation of the bridge structure due to lateral spreading in the vicinity of the abutments. The derived insights indicate a need for such global analysis techniques, when addressing the potential hazard of liquefaction and its consequences.
Studies have revealed that rheological characteristics and self‐weight stress are nonnegligible during a consolidation process, especially for land reclamation projects or dredged soils. However, they are rarely considered simultaneously in traditional consolidation theories. This paper presents a general solution to the consolidation system of rheological soils that incorporates a fractional derivative model and self‐weight stress. First, the theory of the fractional derivative is introduced to the Merchant model to describe the consolidation behaviours of rheological soils, and the self‐weight stress of soils is simultaneously considered. Based on this model, the governing equation of a rheological consolidation system that considers self‐weight stress is obtained. Second, the analytical solutions of the effective stress and settlement in the Laplace domain are obtained by applying the Laplace transform to the consolidation governing equation. Further, the actual solutions in the real domain are obtained by a numerical Laplace transform inversion method (Abate's fixed Talbot method). Finally, the reliability and correctness of the consolidation theories and the proposed solutions are verified by comparing the calculated results with the degenerate solutions and experimental results in the existing literature. Furthermore, parametric studies are conducted to investigate the influence of rheological parameters and self‐weight parameters on the consolidation settlement and consolidation rate.
This paper investigates the nonlinear unscented Kalman filtering (UKF) problem for discrete nonlinear dynamic systems with random parameters. We develop an improved unscented transformation by incorporating the random parameters into the state vector to enlarge the number of sigma points. The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. An application to the mobile source localization with time difference of arrival (TDOA) measurements and sensor position uncertainties is provided where the simulation results illustrate that the improved UKF method leads to a superior performance in comparison with the normal UKF method.
For a compact subset K in the complex plane, let A(K) denote the algebra of all functions continuous on K and analytic on K • and let R(K) denote the uniform closure of the rational functions with poles off K. Let G is a bounded open subset whose complement in the plane has a finite number of components. Suppose that A(G) = R(G) and every function in H ∞ (G) is the pointwise limit of a bounded sequence of functions in R(G). The purpose of this paper is to characterize all subnormal operators similar to Mz, the operator of multiplication by the independent variable z on the Hardy space H 2 (G). We also characterize all bounded linear operators that are unitarily equivalent to Mz in the case when each of the components of G is simply connected. In particular, our similarity result extends a well-known result of W. Clary on the unit disk to multiply connected domains.
Mathematics Subject Classification (2000). Primary 47B20; Secondary 30H05, 30E10, 46E15.
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