Vízügyi Közlemények, 1972 (54. évfolyam)

4. füzet - Rövidebb közlemények és beszámolók

(57) THE MARGIN OF SAFETY DETERMINED BY STATISTICAL ANALYSIS By Dr. Bogárdi, István, Civ. Engr. — Dr. Sziderovszky, Ferenc, Mathematician (For the Hungarian text see pp. 255) In designing engineering projects the uncertainties due to random load variations, fluctuations in the quality of materials, observation records of limited length and to a host of other factors are allowed for by introducing an appropriate factor of safety. A method is suggested herein, which appears useful to minimize the economic losses caused by the uncertainties resulting from observation records of finite length. The factor of safety thus obtained can be applied to the strengthening of existing flood levees, in dimensioning reservoir dams, or in estimating the stand-by capacity of waterworks, irrigation projects, or storage reservoirs. The magnitude of the design discharge, stage or the existing degree of development is known either from earlier economic analyses, or these have been specified by some authority. The design probability pertaining to this value is obtained from the distribution function F(h

) estimated from the observation record of n years length. The value pertaining to the design probability value is far from accurate, but ils empirical distribution can be found by a simulation method. The margin of safety Ah is found by optimization. If the design value is h

0, then the development to h

a +Ah is advisable for which the target function under (2) + (3) + (4) becomes maximum : h[K(h), h(h), Ah] + L[K(h), F(h), Ah] - I

3[k(h*), Ah]-* max where is the elimination of economic loss due to the uncertainty of the distribution function F(h), resulting from the margin of safety _1Л, K(li) is the damage or benefit function, g(h) is the density function of the value pertaining to the design probability, I., is the excess benefit, or averted damage resulting from the margin of safety Ah, I

s is the cost of developing to the margin of safety Ah, where the cost function is k(h). If the distribution F(h) is a normal one, then it is possible to find the expected value and standard deviation of the function g(h) analytically as well. As an example of practical interest the determination of the margin of safety, or the excess degree of protection is illustrated for the levee section along the Tisza River at Polgár. Relations are demonstrated for the margin of safety and the length of the observation record ( Fig. 7), as well as for the level of design probability and the magnitude of uncertainty (Fig. G

). The shorter the record of observation and the higher the benefit accruing from the development, or the greater the damage averted thereby, further the higher the level of design probability is, the wider will be the geometric standard deviation of the function g(h) and consequently the necessary margin, or factor of safety. PROTECTION ZONES FOR THE THERMAL WATERS AT BUDAPEST By Dr. Sárváry, István, Civ. Engr. (For the Hungarian text see pp. 269) The thermal waters at Budapest, the capital of Hungary, emerge partly in natural springs along the Danube, partly in overflowing artesian boreholes sunk at some distance therefrom. The waterbearing rock formation is invariably greatly karstic Triassic dolomite, which forms a coherent base under large parts of the country to the West of the Danube.