Stress distribution in conical sand heaps at incipient failure under active and passive conditions.

• The numerical stress solutions at incipient failure everywhere, for conical sand heaps under both active and passive conditions were successfully solved. • The 5th order adaptive Runge–Kutta method in conjunction with appropriate numerical perturbations and the shooting technique were employed. • The arching effect in an axisymmetric cone was visualized by the trajectories of principal stresses subjected to various repose angles. Stress discontinuity plays an important role in both planar and conical heaps of granular materials. The aim of this study is to reveal the numerical solutions for the stress distribution in fully plastic conical sand heaps that obey the Mohr-Coulomb yield criterion under both passive and active conditions. Levy's circumferential stress assumption was added to the system of equilibrium equations to formulate a pair of ordinary differential equations that were integrated by the 5th order adaptive Runge–Kutta method. Moreover, the numerical perturbations of the initial conditions were put in place to overcome the singularities of the integrations. Trial-and-error iterations were implemented under the passive condition to indicate the location of the stress discontinuity in conjunction with the application of the stress jump condition. Meanwhile, the shooting technique was employed to facilitate the integration under the active condition. The results of the passive conical sand heaps exhibit a local minimum pressure at the center, thus initiating arch action. In addition, the trajectories of principal stresses visually elucidate the mechanisms of load transfer in the conical sand heaps. The linear-fitting relationship between the location of the stress discontinuity and the repose angle in a conical sand heap under the passive condition was also elaborated. [ABSTRACT FROM AUTHOR]