Explicit stress integration with error control for the Barcelona Basic Model.: Part II: Algorithms efficiency and accuracy

The paper compares the accuracy and efficiency of explicit stress integration schemes for elasto-plastic unsaturated soil models with automatic error control. Numerical tests are performed with reference to the Barcelona Basic Model (BBM), one of the most popular elasto-plastic models for unsaturated soils, by using eight explicit Runge–Kutta algorithms of various order as well as a novel application of the extrapolation method described in the companion paper. Initially, the results obtained from the lowest order Runge–Kutta scheme (i.e. Modified Euler) as well as the extrapolation method are checked against accurate solutions of a number of BBM paths involving changes of strains and suction. Subsequently, the efficiency and accuracy of all algorithms are assessed for generic increments of strains and suction, while the difference between two alternative error control methods is also analysed. The results presented, although strictly valid for the Barcelona Basic Model, are expected to be general and relevant to other similar unsaturated elasto-plastic models formulated in terms of two independent stress variables such as net stress and suction.     

Generation and propagation of transient nonlinear waves in a wave flume

A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.     

The influence of track configuration and multibeam echosounder parameters on the accuracy of seabed DTMs obtained in shallow water

This article presents research that aims to assess the accuracy of seabed bathymetry models on the basis of measurements carried out using a multibeam echosounder. It discusses the problem of accuracy assessment which occurs at particular stages of the creation of digital terrain models (DTMs), and analyzes the influence of both the individual multibeam echosounder parameters and the procedures adopted during the survey on the modeling process’s accuracy. Factors that may affect accuracy include the device’s measurement accuracy, the boat speed, the track configuration, the beam width and the selected interpolation method. The article does not deal with errors due to navigation and vessel motion, these being taken to be of the highest possible accuracy. For the research we developed a virtual survey simulator. Recommendations for how to optimize the measurement process while ensuring the created models are of a high quality are presented later in the paper.     

Numerical simulation of catastrophic flood: the case study of hypothetical failure of the Bielkowo hydro-power plant reservoir

The numerical modeling of flood wave propagation following the hypothetical breaks of the embankments of the Bielkowo hydro-power plant storage reservoir (Kolbudy II Reservoir) on the Radunia River in Poland has been presented. The results of computations were used to estimate the parameters of the flood waves, which are indispensable for the flood zone determination and mapping and then for the flood risk analysis. When estimating the reach and area of the inundation, related to the embankments failures, digital terrain model, and mathematical model of flood wave propagation are necessary. For the numerical simulations of flood, the mathematical model of free surface, two-dimensional unsteady water flow was applied. Four locations of potential breaks of the reservoir embankments were considered. The computed flood zones were presented on the flood hazard maps. The maps have been used by the local authorities and the dam owner to manage the flood risk related to hydro-power plants operations on the Radunia River. This type of research has been done for the first time for the water plant managed by the ENERGA Elektrownie Straszyn.     

Non-integrability of the dumbbell and point mass problem

This paper discusses a constrained gravitational three-body problem with two of the point masses separated by a massless inflexible rod to form a dumbbell. This problem is a simplification of a problem of a symmetric rigid body and a point mass, and has numerous applications in Celestial Mechanics and Astrodynamics. The non-integrability of this system is proven. This was achieved thanks to an analysis of variational equations along a certain particular solution and an investigation of their differential Galois group. Nowadays this approach is the most effective tool for study integrability of Hamiltonian and non-Hamiltonian systems.     

Unconfined linear flow to a horizontal well

The validity of a previously proposed but untested modification to equations for flow to a horizontal well is assessed using a specially developed finite-difference model. This modification extends confined flow equations to allow the head in the well and the saturated depth at the well to be estimated in unconfined conditions. The study is limited to the case of two-dimensional flow with no flow in the direction parallel to the line of the well. The results show that the modified equations for both a finite unconfined aquifer and, by inference, an infinite unconfined aquifer are adequately accurate for practical application.     

Three-dimensional seismic modelling of crustal structure in the TESZ region based on POLONAISE''97 data

This paper reports the results of 3-D tomographic modelling of crustal structure in the Trans European Suture Zone region (TESZ) of Poland, eastern Germany and Lithuania. The data are the product of a large-scale seismic experiment POLONAISE'97, which was carried out in 1997. This experiment was designed to provide some 3-D coverage. The TESZ forms the boundary between the Precambrian crustal terranes of the East European Craton (EEC) and the younger Phanerozoic terranes to the southwest. The 3-D results generally confirm the earth models derived by earlier 2-D analyses, but also add some important details as well as a 3-D perspective on the structure. The velocity model obtained shows substantial horizontal variations of crustal structure across the study area. Seismic modelling shows low (<6.1 km/s) velocities suggesting the presence of sedimentary rocks down to a depth of about 20 km in the Polish basin. The shape of the basin in the vicinity of the profile P4 shows significant asymmetry. Three-dimensional modelling also allowed tracing of horizontal irregularities of the basin shape as well as variations of the Moho depth not only along profiles, but also between them. The slice between P2 and P4 profiles shows about 10-km variations of the Moho over a 100-km interval. The crustal thickness varies from about 30 km in SW, beneath the Palaeozoic platform, to about 42 km beneath East European Craton in NE. High seismic velocities of about 6.6 km/s were found in the depth range 2–10 km, which coincides with K trzyn anorthosite massif. The results of this 3-D seismic modelling of the POLONAISE'97 data will ultimately be supplemented by inversion of seismic data from previous experiments.