A stochastic, geostatistic and reliability view on some geotechnical distributions

Abstract

In this paper the following problems are treated: - Estimation of the mean value of a random function Z(x), defined in a stochastic finite element v, (SFE), zv= 1 ∫ ( ) where the distributions of Z(x) at each node are known; - Kriking solution with SFE under the non- stationary hypothesis: E(Z(x))=m(x) , C(x, h) = E{(Z(x+h)Z(x)}-m(x+h)m(x). Finally are given the conclusions underlying the importance of above stochastic instruments not only in the stochastic geotechnical discipline but also in other ones as in energy, geology, geophysics, mechanics, dynamics, elastostatics, finance , engineering , environment, climate etc., in which the distributions are used. 1. Estimation of the mean value of a random function Z(x), defined in a stochastic finite element (SFE) v, zv = 1/v  v Z(x)dx, where the distributions of Z(x) at each node are known; 2. A discretization random field view of SFE in relation to other dicsetized methods. 3. Kriking in SFE view 4. SFE in reliability analysis. 5. Finally some considerations are presented, related to stochastic random field proprieties estimation and stochastic differential equations.