Gamma type random field for silo pressure ∗

Measurements show that silo wall pressures exhibit large fluctuations in time and space during discharge of the silo. This observation is important for the design of the silo wall because spatial pressure variations may impose substantial bending moments that otherwise may be small or vanishing due to the carrying ability of the membrane forces in the silo wall. Information about the stochastic properties of this pressure variation cannot be obtained from any existing continuum model for the silo medium flowing within the confinement of the silo walls. Therefore the modeling must presently be tied to statistical analysis of the empirical evidence combined with simple mechanical principles. This paper summarizes the mathematics of a gamma distribution type random field model resulting from the data analysis and discusses the implications for the reliability analysis of the silo wall. Silo load model. A stochastic silo load model has been formulated in (Ditlevsen & Berntsen 1999) on the basis of pressure cell data obtained during discharge plug flow of barley in a 7 m internal diameter, 40 m high circular concrete silo in Karpalund, Sweden. The statistical analysis of the data combined with equilibrium considerations lead to a stochastic field model that defines the wall pressure p(z, θ) at the dimensionless level coordinate z (i.e. level/ silo radius a) and the angular coordinate θ. The model applies to levels z both sufficiently deep below the medium surface and sufficiently high above the outlet to allow an assumption of statistical homogeneity along a vertical. In the upper part of the medium the field can by a corrective factor be modified to obey Janssens wall pressure formula in the mean such that the pressure becomes zero at the medium surface. The pressure field model is