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By Wolfgang Fellin, Heimo Lessmann, Michael Oberguggenberger, Robert Vieider

This quantity comprehensively addresses the difficulty of uncertainty in civil engineering, from layout to development. present engineering perform frequently leaves uncertainty matters apart, although new medical instruments were constructed long ago a long time that let a rational description of uncertainties of all types, from version uncertainty to information uncertainty. it's the objective of this quantity to take a serious examine present engineering danger ideas so that it will increase understanding of uncertainty in numerical computations, shortcomings of a strictly probabilistic safeguard suggestion, geotechnical versions of failure and their development implications, real development, and obligation. furthermore, many of the new strategies for modelling uncertainty are defined. The ebook is as a result a collaborate attempt of mathematicians, engineers and development managers who met usually in a post-graduate seminar on the college of Innsbruck prior to now years.

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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. After recalling the definitions, we stress their interpretations (semantics), axioms, interrelations as well as numerical procedures and demonstrate how the concepts are applied in practice.

Fits, cumulative distribution functions interval. 09. 454. 2 Spatial and local variation We mention briefly the well-known geotechnical spatial versus local variation problem. On the one hand the strength of the material cannot be measured exactly at each point, and on the other hand the soil is usually spatially inhomogeneous. Both effects contribute to the variability of the data. For the sake of simplicity we assume in this example tan ϕ to be homogeneously distributed in space, but otherwise a random variable with statistical fluctuations.

07) ≤ 10−589 ≈ 0. Less conservative estimates would be obtained by restricting the set of admitted input distributions. Æ Failure probabilities f 45 fS pf Q, S Qf ( ϕ ) Fig. 7. Upper failure probability. 2 Random sets The second idea is to get some valuation of the plausibility of the computed failure probability (cf. (Tab. 7) by means of random set theory. We demonstrate the concepts under two modeling assumptions: we assume that the load is normally distributed according to (2), and we postulate that the friction coefficient ν = tan ϕ has a normal distribution (µν , σν2 ).

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