Empirical Stochastic Silo Load Model. I: Correlation Theory

During the emptying phase silo wall pressures show large random fluctuations in time and space. The nonuniform variations of the pressure along the wall have a decisive influence on the bending moments in the silo wall. It seems difficult to formulate continuum mechanical models to explain these fluctuations that turn out very sensitive to the random geometrical imperfections of the silo wall. This empirical evidence calls for random process and field descriptions of the pressure variations. On the basis of the philosophy of stochastic interpolation, a parametric covariance model with a minimal number of parameters is formulated. The choice of model is guided by the property that in linear regression interpolation the covariance function acts analogously to an interpolating spline function. The covariance model is required to satisfy the equations of equilibrium in any horizontal layer of the silo medium assuming as a reasonable approximation that the horizontal cross section of the medium is without shear force. In the first of two companion papers, the model is adapted to a specific set of measurements from pressure cells situated along a horizontal perimeter of a circular cylindrical concrete silo. In the third paper the model is applied in a reliability analysis example.