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

ISBN-10: 3540222464

ISBN-13: 9783540222460

ISBN-10: 3540268472

ISBN-13: 9783540268475

This quantity comprehensively addresses the problem of uncertainty in civil engineering, from layout to building. present engineering perform usually leaves uncertainty concerns apart, although new clinical instruments were built some time past a long time that let a rational description of uncertainties of all types, from version uncertainty to facts uncertainty. it's the goal of this quantity to take a serious examine present engineering danger suggestions to be able to increase knowledge of uncertainty in numerical computations, shortcomings of a strictly probabilistic security inspiration, geotechnical versions of failure and their development implications, genuine development, and obligation. additionally, a few of the new approaches for modelling uncertainty are defined. The booklet is end result of the a collaborate attempt of mathematicians, engineers and building managers who met usually in a post-graduate seminar on the college of Innsbruck prior to now years.

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**Extra info for Analyzing Uncertainty in Civil Engineering**

**Sample text**

This l would change for every realisation of tan ϕ due to (7). We use the same length l in every realisation by setting ϕm = µϕ = 30◦ in (7). This error is small compared with other uncertainties. 21. Monte-Carlo simulations with c ∼ N(µc , σµ2 c ) and tan ϕ ∼ N(µtan ϕ , σµ2 tan ϕ ) lead to the dashed curve in Fig. 12. Depending on the actual choice µc the Ambiguity of safety deﬁnition in geotechnical models 27 calculations with and without spacial averaging diﬀers up to two orders of magnitude.

Nl Ambiguity of safety deﬁnition in geotechnical models 29 Table 2. Factors of safety η (14) for the slope in Fig. 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).

8. An expression for this distance is ηϕ . Using the Fellenius deﬁnition we measure a third distance, which is represented by η. d ist . 8 Fig. 8. 38 diﬀerence. Using the Euclidean metric the minimal distance can be found perpendicular to the curve deﬁned by the limit state g = 0, which is lower than the distance obtained by η, see Fig. 8. g. if we plot g in a c–ϕ coordinate system, instead of a c–tan ϕ system. All these underlying conventions make the distance interpretation ambiguous. One has to keep in mind that any safety deﬁnition is kind of arbitrary.

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