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By Wolfgang Fellin, Heimo Lessmann, Michael Oberguggenberger, Robert Vieider
This quantity comprehensively addresses the problem of uncertainty in civil engineering, from layout to building. present engineering perform frequently leaves uncertainty concerns apart, even though new clinical instruments were built long ago a long time that let a rational description of uncertainties of every kind, from version uncertainty to facts uncertainty. it's the target of this quantity to take a severe examine present engineering probability options so as to increase information of uncertainty in numerical computations, shortcomings of a strictly probabilistic defense inspiration, geotechnical types of failure and their building implications, real building, and obligation. furthermore, the various new systems for modelling uncertainty are defined. The e-book is due to the a collaborate attempt of mathematicians, engineers and building managers who met frequently in a post-graduate seminar on the college of Innsbruck in past times years.
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Extra resources for Analyzing Uncertainty in Civil Engineering
This causes diﬀerent design states, see Fig. 9. In our particular case a calculation based on EC 7 would predict unsafe conditions, whereas a calculation according to DIN 1054-100 would state safe conditions. Not only the value of the distance between characteristic and design state is diﬀerent, also the direction of the distance is changing when using diﬀerent codes. Again, the deﬁnition of safety is kind of arbitrary. 7 Probabilistic approach The safeties η, ηc and ηϕ generally do not measure the shortest distance between the actual state of the structure to the limit state g = 0, see Fig 10.
Furthermore one can easily estimate variations of the safety due to variations of the input. Example: We calculate the safety factor η for the slope in Fig. 1 with a planar failure surface. 38. 0155 . 34 . 38 From this we see immediately that the safety η is more sensitive to the cohesion than to the friction angle, compare Figs. 5 and 6. 28. 5 Conclusion The wish of an engineer to know (exactly) how far a structure is from collapse cannot be fulﬁlled, at least in geotechnical engineering. The calculated safety of a structure depends on the used mechanical model and the deﬁnition of safety within this model.
One measure of the distance is (c − cm ) with ϕm = ϕ, which appears as vertical distance in Fig. 8. This distance is represented by the safety factor ηc : c − cm = c(1 − 1/ηc ). Another measure is the distance (tan ϕ − tan ϕm ) with cm = c, which is a horizontal distance in Fig. 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.
Analyzing Uncertainty in Civil Engineering by Wolfgang Fellin, Heimo Lessmann, Michael Oberguggenberger, Robert Vieider