Stress propagation and arching in static sandpiles

Journal de Physique II

Volumn 7, Issue 1, 1997, Pages 39-80

  Wittmer, J P ^a   Cates, M E ^a   Claudia, P ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; GRANULAR MATERIALS; MATHEMATICAL MODELS; MECHANICS; PHYSICS; POROUS MATERIALS; SAND; STRESS ANALYSIS;

ARCHING; STATIC SANDPILES; STRESS PROPAGATION;

STRESSES;

EID: 0030648010     PISSN: 11554312     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

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31. In principle one could construct piles in which the scaling was nonetheless obeyed, by demanding that the relative variation of the material properties between (say) an element at the apex, and an element directly beneath the apex at the base, must be the same for all piles. However, this would require the spatial gradient of the size distribution, for the element at the base, to vary inversely with the height of the pile. Clearly, the size distribution (and its gradient) in this element is fixed forever long before the eventual height of the pile is decided. We conclude that, although size segregation may arise, models invoking this to explain the dip are inconsistent with the experiments of reference [2].
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37. A simple method for determining the stress components in two dimensions on a particular plane through a point and comparing them with the yield criterion is known as Mohr's circle [10]. Unfortunately, this method forces an unusual sign convention we do not wish to introduce here.
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39. The tilt axis ^ exactly bisects the angle between the free surface and the vertical (as proved in Sect. 2.2).
40. It turns out that discontinuous derivatives can arise for three values of S: at the outer slope (S = 1); on the central axis of the pile (S = 0); and the point S = SQ where the stress information from the apex of the pile reaches the bottom; examples can be seen in Figure 2a.
41. 2.
42. Note that the RSF scaling, while allowing (in two dimensions) a distinction between the construction histories of elements in the right and left halves of the pile, does not permit any distinction between the elements within one half.
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46. The IFE model is not a special case of OSL; however it turns out that the term cot(0)î7 in equation (21) can be checked a posteriori to be rather small for all 5 and 0 (leading to a quadratic hump, as discussed by BCC). This means that IFE is in some sense "close" to the BCC model on the rj, fj, plane (hence its smooth behaviour at the central axis) even though it lies outside the OSL parameterization.
47. Though an analytic proof should be possible, we have so far only checked this numerically.
48. The "Coulomb yield criterion" is the factional analogue of Tresca's criterion [13]. The frictional analogue of von Mises' criterion is the "Conical yield criterion". For a twodimensional problem both criteria are identical. In three dimensions, the failure conditions predicted by these two criteria only differ slightly and the stresses (calculated for instance with an IFE assumption) are predicted to be similar [10].
49. xx(1).
50. We are grateful to Prof. V. Entov for suggesting this thought-experiment.
51. Rotter J.M., private communication.
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