sandcastles - 1.033/1.57 Recitation Stress Strength October...

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1.033/1.57 Recitation: Stress & Strength October 3, 2003 MIT 1.033/1.57 Fall 2003 Instructor: Franz-Josef ULM Why Sandcastles Fall? We want to study the stress fields in a dry and a humid sandpile, idealized as an inclined semi-infinite half-space oriented at an angle α to the horizontal (see figure below). We choose an x z coordinate system, in which z gives the distance from the surface of the pile ( z > 0 down) and x gives the distance parallel to the surface (infinite extension in the y direction). The sandpile is subjected to its deadweight (volume mass density ρ , and g the earth acceleration vector), and static evolutions are assumed. z x ρ g α Problem Set: Mohr-Coulomb’s problem idealized problem of a sandpile.
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October 3, 2003 page 2 1. Dry Sandpile The Mohr-Coulomb result : We restrict ourselves to solutions which are functions of z alone, i.e., σ = σ ( z ) Furthermore, the sand behavior is assumed isotropic. (a) Determine precisely the conditions which stress field σ needs to satisfy in order to be statically admissible.
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