The local scour around bridge piers influences their stabilities and plays a key role in the bridge failures. The estimation of the maximum possible scour depth around bridge piers is an important step in the design of the bridge pier foundations. In this study, the temporal evolution of local scour depths as well as the equilibrium scour depths were analyzed.
The experiments were carried out in a rectangular flume by using uniform sediment with median diameter of 3.5 mm and geometric standard deviation of 1.4. The diameters of the tested circular bridge piers were 40 mm, 80 mm, 150 mm and 200 mm. The flow and scour depths were determined by ultrasonic sensors. The experiments were realized in clear water conditions with various constant flow rates.
The experimental findings were compared with those calculated from some empirical equations existing in the literature. A new empirical relation involving the flow intensity, the relative water depth and the dimensionless time is also introduced. The advantage of this proposed relation is that the only parameter requiring the calculation is the critical velocity, other parameters being known geometric and hydraulic parameters. The performance of this relation was tested by using experimental data available in the literature, and a satisfactory compatibility was revealed between the experimental and numerical results.
The expressions sufficient condition and necessary condition are frequently used in various areas in sciences (like mathematics, logic, philosophy, natural sciences and social sciences) as well as in everyday usage; therefore, they might be taken as expressing well defined notions which should not lead to any serious misunderstandings when used. According to the widely accepted definitions of both concepts, the concept of sufficient condition and that of necessary condition imply their symmetry (conversion): if one thing poses a sufficient condition to another thing, the latter is a necessary condition for the former; however, this symmetry is hardly intuitive and it is refused by many scholars. Given the analyses of practical examples and a symmetry concept defence test, one may conclude that this view is unfounded. As a result, the definitions of the two notions are not determined enough and so is the question whether there is just a single pair of the notions or whether there are more of them., Výrazy dostatečná podmínka a nezbytná podmínka jsou často používány v různých oblastech vědy (např. Matematika, logika, filosofie, přírodní vědy a společenské vědy) i v každodenním používání; proto mohou být považovány za vyjádření dobře definovaných pojmů, které by při použití neměly vést k vážným nedorozuměním. Podle široce přijímaných definic obou pojmů, pojem dostatečné podmínky a podmínky nezbytné podmínky znamenají jejich symetrii (konverzi): pokud jedna věc představuje dostatečnou podmínku pro jinou věc, ta druhá je nezbytnou podmínkou pro druhou věc; nicméně, tato symetrie je stěží intuitivní a to je odmítnuto mnoha učenci. Vzhledem k analýzám praktických příkladů a obrannému testu koncepce symetrie lze konstatovat, že tento názor není opodstatněný. Jako výsledek,, and František Gahér