A study on the measurement error source of the vertical to horizontal stress ratio on coarse model materials

The correct structural design of storage silos for granular solids depends on the lateral and vertical stresses that are exerted by the stored solids on the silo walls. Standard structural design specifications are reported in international design codes as Eurocode EN 1991-4:2006 [1] and in related national standards. The estimate of the load that acts on a vertical silo wall is usually performed by applying the Janssen [2] method of differential slices, which requires the evaluation of the horizontal to vertical stress ratio or the lateral pressure ratio, K. An experimental device for the measurement of the horizontal to vertical stress ratio had been purposely built and tested for fine and cohesive solids [3]. With powder testing the source of error in measurement procedure for powder flow properties may arise from different sources and, in particular from a) the story of the powder sample or b) some forces not properly accounted in the measurement, such as those due to unduly neglected frictions. Proper measurement procedures should determine measurement conditions in which both sources of errors are minimized or appropriately accounted for. For example, for the developed device [3], it was found that that a twisting action on the lid of the cylindrical powder cell was able to produce reliable repeatable results, by possibly minimizing both the effect of the powder history and of the uncounted powder friction on the cell lid. In order to asses on the possible sources of errors in the proposed experimental procedures a large set of experiments was carried out by using model material made of Glass spheres (6mm), plastic spheres (5 mm), steel spheres (2mm). Comparison on the scatter of the value of the vertical to horizontal stress ratio obtained within a single experiment at different load values and the scatter of data between different sets of experiments it can be concluded that with these materials the largest source of error is due to unpredictable differences in the internal structure of the particulate materials. Furthermore, the comparison between the Coulomb representation of the flow properties of the particulate solids and the Mohr representation of the state of stress in the device obtained by assuming the vertical and the horizontal stress as principal stresses confirms the hypothesis that the condition of incipient internal shear of the material is reached by showing Mohr circles tangent to the yield locus. This conditions confirms that the proposed measurement procedure is in fact able to minimize the effects of the lid friction on the sample. Well known hysteresis effects in the unloading part of the experiments are also observed in our experiments and reported. It is verified that, for the tested material, no memory of the previous compression experiment is found only in the case in which the complete sample unloading is reached between the two subsequent experiments. References [1] Eurocode 1. DD ENV 1991-4 (1996). [2] Janssen, H.A. Zeitschr. d. Vereines deutscher Ingenieure, 39, 1045-1049 (1895). As reported by Sperl, M., Granular Matter 8, 59-65 (2006). [3] Barletta, D. and Poletto M. Granular Matter 15, 487–497 (2013).