By Wolfgang Fellin (auth.), a.o. Univ.-Prof. Dipl.-Ing. Dr. Wolfgang Fellin, em. Univ.-Prof. Dipl.-Ing. Heimo Lessmann, a.o. Univ.-Prof. Dr. Michael Oberguggenberger, Dipl.-Ing. Robert Vieider (eds.)
This quantity addresses the difficulty of uncertainty in civil engineering from layout to development. mess ups do take place in perform. Attributing them to a residual procedure hazard or a defective execution of the venture doesn't thoroughly conceal the variety of factors. a more in-depth scrutiny of the followed layout, the engineering version, the knowledge, the soil-construction-interaction and the version assumptions is needed. frequently, the uncertainties in preliminary and boundary stipulations are considerable. present engineering perform usually leaves those concerns apart, even though new clinical instruments were constructed long ago many years that permit a rational description of uncertainties of all types, from version uncertainty to info uncertainty. it's the goal of this quantity to have a serious examine present engineering danger strategies that allows you to bring up understanding of uncertainty in numerical computations, shortcomings of a strictly probabilistic security notion, geotechnical versions of failure mechanisms and their implications for development administration, execution, and the juristic query of accountability. additionally, the various new tactics for modelling uncertainty are defined. The publication is due to the a collaborate attempt of mathematicians, engineers and building managers who met on a regular basis in a submit graduate seminar on the collage of Innsbruck up to now years.
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Serienuntersuchungen zum Vergleich verschiedenener Rahmenscherger¨ ate. Institut f¨ ur Bodenmechanik und Felsmechanik der Universit¨at Karlsruhe, personal communication, 1996.  H. B¨ uhlmann. Mathematical Methods in Risk Theory. Springer-Verlag, Berlin 1970.  G. De Cooman, T. Fine, and T. Seidenfeld, editors. ISIPTA’01, Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications. Shaker Publishing BV, Maastricht, 2001. H. Einstein. Quantifying uncertain engineering geologic information.
20] A. Weißenbach, G. Gudehus, and B. Schuppener. Vorschl¨age zur Anwendung des Teilsicherheitskonzeptes in der Geotechnik. Geotechnik, Sonderheft:4–31, 1999. The mathematics of uncertainty: models, methods and interpretations Michael Oberguggenberger Institut f¨ ur Technische Mathematik, Geometrie und Bauinformatik, Universit¨at Innsbruck Summary. This article discusses various mathematical theories that have been put forth as tools for modelling uncertainty, among them probability, interval arithmetic, random sets, and fuzzy sets.
1 calculated with diﬀerent mechanical models; c = 11 kN/m2 and ϕ = 30◦ . 21 c g =0 ( c, tan ϕ ) tan ϕ Fig. 16. Uncertainties in geotechnical safety assessment: Additional to the uncertainty of the mean values of the shear parameters (rectangular area bounded with dashed line with (c, tan ϕ) the lower bounds of the conﬁdence intervals) there is a possible range of limit state function due to diﬀerent mechanical models (area between solid curves). ∆η ≈ ∂η ∂c ∆c + c,ϕ ∂η ∂ϕ ∆ϕ . (27) ϕ ∆ϕ . η ϕ (28) c,ϕ We bring this in dimensionless form ∂η ∆η ≈ η ∂c c,ϕ =: kc ∂η c ∆c + η c ∂ϕ c,ϕ =: kϕ and deﬁne the dimensionless gradients kc and kϕ .