Slope Instability of the Earthen Levee in Boston, UK: Numerical Simulation and Sensor Data Analysis

The paper presents a slope stability analysis for a heterogeneous earthen levee in Boston, UK, which is prone to occasional slope failures under tidal loads. Dynamic behavior of the levee under tidal fluctuations was simulated using a finite element model of variably saturated linear elastic perfectly plastic soil. Hydraulic conductivities of the soil strata have been calibrated according to piezometers readings, in order to obtain correct range of hydraulic loads in tidal mode. Finite element simulation was complemented with series of limit equilibrium analyses. Stability analyses have shown that slope failure occurs with the development of a circular slip surface located in the soft clay layer. Both models (FEM and LEM) confirm that the least stable hydraulic condition is the combination of the minimum river levels at low tide with the maximal saturation of soil layers. FEM results indicate that in winter time the levee is almost at its limit state, at the margin of safety (strength reduction factor values are 1.03 and 1.04 for the low-tide and high-tide phases, respectively); these results agree with real-life observations. The stability analyses have been implemented as real-time components integrated into the UrbanFlood early warning system for flood protection

Equilibrium spherically curved 2D Lennard-Jones systems

To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N<800) equilibrium configurations are traced as a function of the curvature radius R. Sharp jumps for tiny changes in R between trajectories with major differences in topological structure correspond to avalanche-like transitions. For a typical case, N=25, equilibrium configurations fall on smooth trajectories in state space which can be traced in the E-R plane. The trajectories show-up with local energy minima, from which growth in N at steady curvature can develop.Comment: 10 pages, 2 figures, to be published in Journal of Chemical Physic

Reducing cross-flow vibrations of underflow gates: experiments and numerical studies

An experimental study is combined with numerical modelling to investigate new ways to reduce cross-flow vibrations of hydraulic gates with underflow. A rectangular gate section placed in a flume was given freedom to vibrate in the vertical direction. Holes in the gate bottom enabled leakage flow through the gate to enter the area directly under the gate which is known to play a key role in most excitation mechanisms. For submerged discharge conditions with small gate openings the vertical dynamic support force was measured in the reduced velocity range 1.5 < Vr < 10.5 for a gate with and without holes. The leakage flow through the holes significantly reduced vibrations. This attenuation was most profound in the high stiffness region at 2 < Vr < 3.5. Two-dimensional numerical simulations were performed with the Finite Element Method to assess local velocities and pressures for both gate types. A moving mesh covering both solid and fluid domain allowed free gate movement and two-way fluid-structure interactions. Modelling assumptions and observed numerical effects are discussed and quantified. The simulated added mass in still water is shown to be close to experimental values. The spring stiffness and mass factor were varied to achieve similar response frequencies at the same dry natural frequencies as in the experiment. Although it was not possible to reproduce the vibrations dominated by impinging leading edge vortices (ILEV) at relatively low Vr, the simulations at high Vr showed strong vibrations with movement-induced excitation (MIE). For the latter case, the simulated response reduction of the ventilated gate agrees with the experimental results. The numerical modelling results suggest that the leakage flow diminishes the whipping effect of fluctuations at the trailing edge associated with the streamwise pressure drop across the gate and the body's vertical oscillatory motion.Comment: 27 pages, 15 figures, 2 table

Evolutionary Design of Numerical Methods: Generating Finite Difference and Integration Schemes by Differential Evolution

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration methods. The coefficients are reverse engineered based on samples from a target function and its derivative used for training. The Runge-Kutta schemes are trained using the order condition equations. An appealing feature of the evolutionary method is the low number of model parameters. The population size, termination criterion and number of training points are determined in a sensitivity analysis. Computational results show good agreement between evolved and analytical coefficients. In particular, a new fifth-order Runge-Kutta scheme is computed which adheres to the order conditions with a sum of absolute errors of order 10^-14. Execution of the evolved schemes proved the intended orders of accuracy. The outcome of this study is valuable for future developments in the design of complex numerical methods that are out of reach by conventional means.Comment: 19 pages, 7 figures, 10 tables, 4 appendice