# Load Distribution in Granular Media

*by*Shailendra N. Endley, Soil Engr.; McClelland Engrs., Houston, Tex.,

Alain H. Peyrot, (M.ASCE), Assoc. Prof. of Civ. and Environmental Engrg.; Univ. of Wisconsin, Madison, Wisc.,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1977, Vol. 103, Issue 1, Pg. 99-111

**Document Type:**Journal Paper

**Abstract:**

An impression of the stress distribution in granular media subjected to point loads is determined by integrating the probability laws of particle stiffnesses and points of contact. The first step is to calculate the probability that a load path originating at a concentrated source reaches a specified volume in exactly N steps and that, at the same time, the flexibility of the entire path is contained between specified limits. The joint probability law (number of steps - flexibility) is obtained by a modification of the probability calculus developed by Chandrasekhar to solve random flights problems. Finally, the joint distribution is used to calculate expected values of magnitude and direction of all the forces entering a specified volume. These expected values are directly related to stresses. The probabilistic theory yields stress distributions that are identical to those obtained assuming an homogeneous elastic medium using Boussinesq theory.

**Subject Headings:**Load distribution | Probability | Stress distribution | Load factors | Granular materials | Probability distribution | Joints | Particle size distribution

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