Soils spatial variability types

The OSL model was constructed in order to explain curious observations reporting that the maximum pressure P in a sandpile was not necessarily directly below the pile s peak but, rather, could occur on a ring of nonzero radius [49-52] (see also Savage [53]). In some cases, the pressure at the base was actually reported to have a local minimum under the peak, the so-called stress dip phenomenon. The 2D OSL model has a Janssen-like constitutive relation of the form (Jxx = ( zz + where z is the vertical and x is the horizontal direction. When coupled with the constraint of stress balance, this leads to the proposal that (static) stresses within a granular material satisfy a hyperbolic PDF in the spatial variables, x and z. Bouchaud et al. then showed that this model could predict a stress dip. Savage [53] argued that soil mechanics models [14] can also account for a stress dip. Elasto-plastic soil mechanics models [ 14] are elastic below yield and are described in this case by elliptic equations (above yield, they are characterized by hyperbolic equations). Hence, the OSL and soil mechanics approaches are inherently different types of models. 

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