Realibility of Silo Ring Under Lognormal Stochastic Pressure Using Stochastic Interpolation

Abstract

A Gaussian stochastic silo load model for circular cells has been formulated and used for reliability analysis in two previous papers. In order to avoid negative stresses orthogonal to the wall the possibility of modeling the wall stresses by a non- Gaussian field such as the lognormal field is considered herein. Several fundamental problems by such modeling are revealed. These problems concern the mandatory nonnegativity properties of the covariance structure under certain equilibrium restrictions. However, the investigations also show that the distribution assumption has a substantial influence on the reliability results in spite of the intuitive (but unjustified) reliance on the validity of the central limit theorem for integrals of random fields.

For the practical reliability analysis of the silo wall it is necessary to make a discretization of the random field into another random field defined in terms of a finite, but not too large, set of correlated random variables. It turns out to be essential for the discretization replacement to base it on stochastic interpolation in a particular form. In order to gain insight into the problem the mechanical part of it is kept simple by solely considering the analysis for a ring imagined to be cut out by two consecutive horizontal planes an infinitesimal distance apart at a place far away from regions of the silo with end effects on the internal forces.

The reliability analysis is made with respect to the initial formation of a yield hinge among a finite set of cross-sections. Moreover, a reliability analysis with respect to the development of a collapse mechanism in the ring is considered. The influence of the correlation length (scale of fluctuation) on the reliability is illustrated for both types of limit states. All reliability calculations are made by the standard methods FORM, SORM using the DNV (Det Norske Veritas) program PROBAN.