A linear, analytical solution to the principal stress cap, force balance equations for asymmetrical stresses in cylindrical silos

Abstract

A linear, analytical solution to the principal stress cap force balance equations for asymmetrical stress in a circular silo has been derived. Principal stress relationships are linearly through gradients J1 and J2 and intercepts T1 and T2.The solution gives first-order ordinary differential equations in Z over the principal stress cap surface. The solution to the equation can either be Janssenian(stresses approach limiting values), or exponential(stresses increase exponentially with depth).Exponential stress can be caused by•reversal of the direction of vertical shear stress from upwards(positive) for Janssenian: to downwards(negative) for exponential(vertical stress reversal exponential stress).and/or•the inclination of the principal stress cap (λ-line) directing gravitational forces to the lower region of the stress cap(σ2 exponential stress).Symmetrical systems; systems with low Eccentricity; and concave systems give Janssenian stress throughout with the appropriate state of stress (passive/convex; active/concave).Exponential stress systems could cause high stresses and large variations around the perimeter of the silo, with potentially catastrophic effects.The model is relatively simple and can form a basis for the planning and design of experiments, and a base case for more sophisticated models.