Andrew Drescher

Arching in hoppers. I: Arching theories and bulk material flow properties

In this paper, the first in a series of two, the theories of arching in symmetrical hoppers are discussed in terms of the underlying assumptions related to flow properties of bulk materials. In particular, the link between the form of the instantaneous and effective yield conditions, and the form of the flow function is investigated in detail, and the resulting implications in the arching theories are critically assessed. It is demonstrated that approximations involved in flow properties determination may contradict the assumptions in the arching theory used. The analysis is supplemented with results of direct shear tests on limestone, gypsum, coal, cement, and taconite, which are subsequently used to illustrate the required approximations. Also, some modifications to the existing arching theories are discussed. In a companion paper, the results of this paper are used to predict the value of outlet size critical for arching, which is next compared with results of mid-scale model tests on plane (wedge-type) and conical hoppers.

Modeling plug flow in bins/hoppers

In bin/hoppers filled with densely packed bulk materials, upon opening of the outlet, a narrow plug-type flow zone propagates upward and widens. With progressing discharge, this zone grows, eventually reaching the top of the material and possibly the walls of the bin. Based on small-scale model tests, a theoretical model of the evolution of the plug flow zone in plane and axisymmetric bin/hoppers is presented. The model is purely kinematic and approximate; however, it accounts for the observed lower than initial density of the flowing material, and the general form of the flow pattern. This is accomplished by separating flow into two regions, radial and vertical, separated from the stagnant material by density shocks. Comparison between the model and plane flow experiments shows satisfactory agreement providing additional assumptions relating the radial and vertical flow are introduced. The model may find application in predicting transition from plug to mass flow.

TIRE-INDUCED SURFACE STRESSES IN FLEXIBLE PAVEMENTS

Site observations of flexible-pavement distress in various countries indicate frequent occurrence of longitudinal cracking in the top asphalt concrete layer. Analytic and numerical studies of multilayer elastic systems subject to wheel loads have linked longitudinal cracking to surface tensile stresses. However, due to the complexity of tire-pavement interaction resulting from tire geometry and loading conditions, accurate and fully representative distribution of surface stresses remains partly unknown. An attempt is made to provide information on surface stresses that derives from both theory and experiments. In particular, contact mechanics solutions are analyzed to gain information on loads that are subsequently used in performing numerical evaluation of surface stresses. Examples of three-dimensional computations using the finite-element code ABAQUS illustrate the analysis. The results indicate a greater potential for tensile stresses outside the tire treads than in the middle of the treads.

Stiffness Estimates Using Portable Deflectometers

The use of falling weight deflectometers and portable falling weight deflectometers (PFWDs) is now common for field characterization of pavement system layers. In particular, the application of portable deflectometers in quality assurance of newly constructed granular base has become more widespread. Typically, these devices are used for an in situ assessment of the Youngs modulus of the base layer. The traditional backcalculation uses an elastostatic half-space framework to relate Youngs modulus of the pavement foundation to the stiffness estimates obtained from force and velocity measurements. The data interpretation method that is customarily used for stiffness estimation uses peak values of the force and displacement records in lieu of their static counterparts. The performance of a particular device, PRIMA 100, was examined with the newly developed beam verification tester (BVT) of known static stiffness. It was shown that the conventional, peak-based method of backanalysis produces incorrect estimates of the static stiffness of the BVT. An alternative, spectral-based data interpretation method was proposed. This method, based on (a) concept and measurement of the frequency response function and (b) a single-degree-of-freedom mechanical model, was employed to extract the true static stiffness from PRIMA 100 measurements. The results show a good agreement between the true static stiffness of the BVT and its PFWD estimates stemming from the modified approach. The BVT apparatus can therefore be used to assess the performance of the sensors and data interpretation of PRIMA 100-type deflectometers.

Arching in hoppers: II. Arching theories and critical outlet size

This paper, the second in a series of two, describes medium scale tests on symmetrical, plane (wedge-type) and conical hoppers aimed at determining the critical outlet size preventing the formation of arches or domes during gravitational discharge of bulk materials. The bulk materials used were limestone, gypsum, coal, cement, and taconite, and their flow properties are described in the first paper of the series. The experimentally-determined outlet size is compared with theoretical predictions based on several existing theories of arching. It is shown that all theories overestimate the outlet size by a factor of about 2 to 4, and the results are discussed in the light of flow parameters value and modifications of the theories.

Interpretation of Indirect Tension Test Based on Viscoelasticity

The diametral indirect tension test is a convenient configuration for determining the modulus of asphalt concrete samples. The resilient modulus test has been a traditional approach to characterizing the stiffness of asphalt concrete, but it leaves much to be desired when considering the viscous behavior this material exhibits, even at low temperatures. A method for determining the complex compliance, complex modulus, and phase angle of asphalt mixtures using the indirect tensile test and a haversine load history is presented here. This test may be performed over a range of frequencies and temperatures as demonstrated on materials used in the Minnesota Road Research Project. The use of the haversine loading simplifies the test when compared with the pulse loading and rest time used in the resilient modulus test, and it allows for the characterization of the elastic and viscous components of the materials overall behavior, which is very difficult, at best, with the current test methods.

TRIAXIAL BEHAVIOR OF REFINED SUPERIOR SAND MODEL

Abstract The note considers the response of the elasto-plastic refined Superior sand model to monotonic loading in triaxial compression tests. The model was proposed by Drescher and Mroz [Drescher A, Mroz Z. A refined superior sand model. In: Pietruszczak S, Pande GN, editors. Numerical models in geomechanics NUMOG VI. Rotterdam: Balkema, 1997. p. 21–6.] to describe static liquefaction in granular deposits, and in particular the effective undrained stress path in which the shear stress increases, decreases, and again increases with increasing strains. A novel evolution law in the hardening rule is introduced which reduces the number of parameters, and allows for describing the experimentally observed behavior of loose, medium dense, and dense granular deposits both in the undrained and drained loading. When compared with experiments, the model prediction is fairly satisfactory. Further modifications of the model are discussed.

A theoretical analysis of channeling in bins and hoppers

Abstract The kinematic approach of limit analysis suggested by Drescher [7] is adopted to derive a criterion for channeling in cylindrical bins and conical hoppers. The bulk material is modeled as a perfectly plastic solid with the flow rule associated or non-associated with the Mohr—Coulomb yield condition, which is modified by a tension cut-off. The channeling criterion is derived by examining the stability of bulk material surrounding an empty channel. Partial failure mechanisms are considered, and the influence of the material/wall interface on the stability is discussed.

Analysis of compression of short cylinders of Coulomb material

Abstract A static solution is presented for the case of compression of short circular cylinders between rough, rigid plates. It is assumed that the material is perfectly plastic, satisfying the Coulomb yield condition and the associated flow law. The stress state is calculated for the edge regime of the Coulomb hexagon for which the Haar-Karman hypothesis is satisfied. The solution is obtained for several height-diameter ratios, various friction conditions at the cylinder-plate interface and for various angles of internal friction. Results of theoretical solutions are compared with available experimental data. The analysis may be useful in experimental determination of the angle of internal friction and cohesion by compressing short cylinders between rigid plates.

Rate Effects in the Superior Sand Model

This paper aims at analyzing the response of the elasto-viscoplastic model Superior sand proposed by Boukpeti et al. for describing rate effects in undrained loading of loosely-packed granular deposits. The equations governing the model in triaxial compression are solved for three loading histories: constant strain rate, constant stress rate, and creep. The resulting stress-strain-time curves are discussed in the light of material instability states in relation to static liquefaction. It is shown that the classical second-order work rate instability criterion is no longer valid, and a new criterion based on the deformation acceleration is presented.