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 usually leaves uncertainty concerns apart, although new medical instruments were built long ago a long time that let a rational description of uncertainties of all types, from version uncertainty to information uncertainty. it's the goal of this quantity to take a serious examine present engineering chance thoughts for you to bring up know-how of uncertainty in numerical computations, shortcomings of a strictly probabilistic defense proposal, geotechnical types of failure and their building implications, real building, and obligation. additionally, a few of the new techniques for modelling uncertainty are defined. The ebook is as a result a collaborate attempt of mathematicians, engineers and building managers who met on a regular basis in a post-graduate seminar on the collage of Innsbruck in the past years.
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Additional info for Analyzing Uncertainty in Civil Engineering
Thus, the mean value µ lies within an interval, of which the lower boundary is the characteristic value. Typical intervals may be µc = [11 . . 23] kN/m2 µϕ = [30 . . 35] ◦ . (24) (25) If statistical data were available (24) and (25) would be chosen as conﬁdence intervals. 4; σ = µV . We further assume that Vϕ = Vtan ϕ . 26 Wolfgang Fellin Monte-Carlo simulations applied to the limit state function (8) with deterministic γ = 16 kN/m3 , normally distributed c ∼ N(µc , σc2 ) and tan ϕ ∼ 2 N(µtan ϕ , σtan ϕ ) results in the solid line in Fig.
The sign of k indicates if a cautious estimate of a parameter is gained by reducing (if k > 0) or increasing (if k < 0) the mean value. 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.
645. 75 kN . (2) Numerical simulation: A conceptually simple method for computing the failure probability is Monte-Carlo simulation, with which we begin our elaboration. In this special example, the failure probabilities actually can be expressed analytically by a single integral; this will be presented in a later paragraph. The Monte-Carlo simulations were done with the aid of a Fortran-program using the random number generators for a uniform distribution Í(l, u) (for high number of calls N > 108 ) and a normal distribution Æ(0, 1) published in .