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Linear and nonlinear stress propagations in the problem of two-dimensional symmetrical sand pile were investigated. The hyperbolic-type differential equations were formulated under the criterion of self-weight loading. This study shows that the admissible stress solution can be obtained from a wave-like equation by combining the differential equilibrium equations and the local stress conditions with the boundary conditions. Unlike linear stress propagation which appears in straight line, nonlinear stress propagation appears in smooth curves of principal stress directions which are regarded as nests of major and minor arches formed in granular media. The spatial distribution of safety factor against sliding under each closure is also presented and discussed.

Admissible Stress Fields for a Semi-infinite Planar Heap of Granular Medium Possessing Self-weight in Loose Condition