On the stability of columns subjected to non-stationary random or deterministic support motion

The dynamic stability of an elastic column subjected to random or deterministic support motion is studied via the Liapunov method. The definitions of mean square stability and the related theorems are presented. Several criteria regarding the stability of the equilibrium state of the column are established. It is shown that if the static axial loading is less than the Euler critical load and the base acceleration is absolute integrable in the mean for random motion of the support or simply absolute integrable for deterministic motion of the base, the equilibrium state of the column is stable.     

Crack propagation trajectories for rocks under mixed mode I-II fracture

Propagation of a crack in engineering materials including rocks can cause failure. Knowledge of the stress state under which a crack can propagate, and the trajectory it may follow during its growth are thus very important for the stability of rock masses/materials and for the safe design of structures in/on rocks. In this paper, the crack initiation angle and subsequent crack propagation path are experimentally investigated for limestone rock specimens. This investigation was conducted under various mixed mode I-II loading conditions, including pure mode-I and pure mode-II.This study includes conducting diametrical compression tests on notched Brazilian disk specimens. Moreover, the effect of confining pressure and temperature on crack initiation and propagation were also studied. The experimental results were compared with theoretical predictions of crack initiation angle. The results showed that limestone behaves in brittle fashion, and the effects of confining pressure and temperature on failure trajectories were not significant. Generally, the crack initiation angle can be predicted by the maximum tangential stress criterion. However, for notched Brazilian disk with high value of crack orientation with respect to loading direction, crack does not propagate from the tip of the crack. This important observation indicated that the tensile-strength failure can become more critical than the fracture-toughness failure.     

Delineation of seismic zonation using fractal modeling in West Yazd province,Central Iran

This study is an attempt to identify seismic zones utilizing number-size (N-S) and concentration-area (C-A) fractal models in the West Yazd province, Central Iran. The analysis was based on the earthquakes’ magnitude and Quaternary faults’ density. Fault density map was generated and classified by fractal modeling. The result indicates that the main fault densities correlate with Dehshir and Eqlid faults. Furthermore, the areas with relatively large earthquake magnitudes are located in the SE and NE parts of the region. The Quaternary faults’ density and earthquake magnitudes were weighted based on the results of the fractal modeling. Finally, weighted maps were combined and classified to show that Dehshir fault has the main role for seismicity in this area. Comparison between results derived via the fractal modeling and conventional seismic zonation map is satisfactory. Furthermore, fractal modeling approach distinguishes different seismic zones with higher accuracy in smaller areas. For validation of results, earthquakes since 2012 were collected and associated with seismic zones. These earthquakes which are correlated with major seismic zones are mainly located near the Dehshir and main Zagros faults.     

Time-dependent seismic hazard analysis for the Greater Tehran and surrounding areas

This study presents a time-dependent approach for seismic hazard in Tehran and surrounding areas. Hazard is evaluated by combining background seismic activity, and larger earthquakes may emanate from fault segments. Using available historical and paleoseismological data or empirical relation, the recurrence time and maximum magnitude of characteristic earthquakes for the major faults have been explored. The Brownian passage time (BPT) distribution has been used to calculate equivalent fictitious seismicity rate for major faults in the region. To include ground motion uncertainty, a logic tree and five ground motion prediction equations have been selected based on their applicability in the region. Finally, hazard maps have been presented.     

Wave-tide interaction modulates nearshore wave height

Ocean Dynamics - The combined hazard of large waves occurring at an extreme high water could increase the risk of coastal flooding. Wave-tide interaction processes are known to modulate the wave...     

The Interface Configuration of the Fresh‐/Dead Sea Water – Theory and Measurements

The high‐density Dead Sea water (1.235 g/cm³) forms a special interface configuration with the fresh groundwater resources of its surrounding aquifers. The fresh groundwater column beneath its surroundings is around one tenth of its length compared to oceanic water. This fact alone indicates the vulnerability of the fresh groundwater resources to the impacts of changes in the Dead Sea level and to saltwater migration. Ghyben‐Herzberg and Glover equations were used to calculate the volumes of water in coastal aquifers which were replaced by freshwater due to the interface seaward migration as a result of the drop in the level of the Dead Sea. For that purpose, the dynamic equation of Glover approach has been integrated to accommodate that type of interface readjustment. The calculated amounts of freshwater which substituted salt Dead Sea water due to the migration of interface are 3.21 · 10¹¹ m³, from a Dead Sea level of –392 m to τ411 m below sea level. The average porosity of coastal aquifers was calculated to range from 2.8 to 2.94%. Geoelectric sounding measurements showed that areas underlying the coastal aquifers formerly occupied by the Dead Sea water are gradually becoming flushed and occupied by freshwater. The latter is becoming salinized due to the residuals of Dead Sea water in the aquifer matrix, the present salinity of which is lower than that of the Dead Sea water. At the same time salt dissolution from the Lisan Marl formation is causing collapses along the shorelines in the form of sinkholes, tens of meters in diameter and depth.     

Discrimination of Mineralized Rock Types in a Copper-Rich Volcanogenic Massive Sulfide Deposit Through Fast Independent Component and Factor Analysis

Natural Resources Research - Multivariate methods are useful for simplifying the interpretation of variables in geochemical data and are widely used to uncover relationships between elements that...     

Vibration analysis of rectangular Mindlin plates on elastic foundations and vertically in contact with stationary fluid by the Ritz method

In this study Free vibration analysis of vertical rectangular Mindlin plates resting on Pasternak elastic foundation and fully or partially in contact with fluid on their one side is investigated for different combinations of boundary conditions. The plate is assumed to be one of vertical rectangular walls of a container in contact with fluid. In order to analyze the interaction of the Mindlin plate with the elastic foundation and fluid system, three displacement components of the plate are expressed in the Ritz method by adopting a set of static Timoshenko beam functions satisfying geometric boundary conditions in a Cartesian co-ordinate system. The method of separation of variables and the method of Fourier series expansion is used to model fluid and to obtain the exact expression of the motion of fluid in the form of integral equations. The fluid domain is finite in depth and width but infinite in the length direction. To demonstrate the accuracy of the present solution, convergence study is first carried out and then a few comparison studies are carried out with the available data in the literature. Finally, natural frequencies of rectangular plates are presented in tabular and graphical forms for different fluid levels, foundation parameters, aspect ratios, thickness to width ratios and boundary conditions.     

Unstable modes of non-axisymmetric gaseous discs

We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter ε. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the response spectrum. We demonstrate that wave interaction in unstable discs, with small initial asymmetries, can develop dense clumps during the phase of exponential growth. Local clumps, which occur on the major spiral arms, can constitute seeds of gas giant planets in accretion discs.