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Title: Normal stress effects in the gravity driven flow of granular materials

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Publication Date:
Research Org.:
National Energy Technology Lab. (NETL), Pittsburgh, PA, and Morgantown, WV (United States). In-house Research
Sponsoring Org.:
USDOE Office of Fossil Energy (FE)
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0020-7462; PII: S0020746217300628
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: International Journal of Non-Linear Mechanics; Journal Volume: 92; Journal Issue: C
Country of Publication:
United States
Granular materials; Normal-stress effects; Maximum packing; Shear-thinning fluid; Second grade fluids; Continuum mechanics

Citation Formats

Wu, Wei-Tao, Aubry, Nadine, Antaki, James F., and Massoudi, Mehrdad. Normal stress effects in the gravity driven flow of granular materials. United States: N. p., 2017. Web. doi:10.1016/j.ijnonlinmec.2017.03.016.
Wu, Wei-Tao, Aubry, Nadine, Antaki, James F., & Massoudi, Mehrdad. Normal stress effects in the gravity driven flow of granular materials. United States. doi:10.1016/j.ijnonlinmec.2017.03.016.
Wu, Wei-Tao, Aubry, Nadine, Antaki, James F., and Massoudi, Mehrdad. Thu . "Normal stress effects in the gravity driven flow of granular materials". United States. doi:10.1016/j.ijnonlinmec.2017.03.016.
title = {Normal stress effects in the gravity driven flow of granular materials},
author = {Wu, Wei-Tao and Aubry, Nadine and Antaki, James F. and Massoudi, Mehrdad},
abstractNote = {},
doi = {10.1016/j.ijnonlinmec.2017.03.016},
journal = {International Journal of Non-Linear Mechanics},
number = C,
volume = 92,
place = {United States},
year = {Thu Jun 01 00:00:00 EDT 2017},
month = {Thu Jun 01 00:00:00 EDT 2017}
  • An approximate solution is presented to the problem of calculating the flow of a cohesionless granular material in a conical hopper such as that used in some coal gasifiers. Treating the material as a perfectly plastic continuum (thus satisfying the Mohr-Coulomb yield condition), the model describes the behavior of granular material in fairly good agreement with experimental data. Intended for application to a mass-flow hopper only, the model is most effective on hoppers with small hopper angles. The model and experimental results deviate at large hopper angles.
  • Hilly or mountainous topography influences gravity-driven groundwater flow and the consequent distribution of effective stress in shallow subsurface environments. Effective stress, in turn, influences the potential for slope failure. To evaluate these influences, the authors formulate a two-dimensional, steady state, poroelastic model. The governing equations incorporate groundwater effects as body forces, and they demonstrate that spatially uniform pore pressure changes do not influence effective stresses. They implement the model using two finite element codes. As an illustrative case, they calculate the groundwater flow field, total body force field, and effective stress field in a straight, homogeneous hillslope. The total bodymore » force and effective stress fields show that groundwater flow can influence shear stresses as well as effective normal stresses. In most parts of the hillslope, groundwater flow significantly increases the Coulomb failure potential {Phi}, which we define as the ratio of maximum shear stress to mean effective normal stress. Groundwater flow also shifts the locus of greatest failure potential toward the slope toe. However, the effects of groundwater flow on failure potential are less pronounced than might be anticipated on the basis of a simpler, one-dimensional, limit equilibrium analysis. This is a consequence of continuity, compatibility, and boundary constraints on the two-dimensional flow and stress fields, and it points to important differences between our elastic continuum model and limit equilibrium models commonly used to assess slope stability.« less
  • Hillslope morphology, material properties, and hydraulic heterogeneities influence the role of groundwater flow in provoking slope instability. The authors evaluate these influences quantitatively by employing the elastic effective stress model and Coulomb failure potential concept described in their companion paper. Sensitivity analyses show that of four dimensionless quantities that control model results, slope profiles and hydraulic conductivity contrasts have the most pronounced and diverse effects on groundwater seepage forces, effective stresses, and slope failure potentials. Gravity-driven groundwater flow strongly influences the shape of equilibrium hillslopes, which they define as those with uniform near-surface failure potentials. For homogeneous slopes with nomore » groundwater flow, equilibrium hillslope profiles are straight; but with gravity-driven flow, equilibrium profiles are concave or convex-concave, and the largest failure potentials exist near the bases of convex slopes. In heterogeneous slopes, relatively slight hydraulic conductivity contrasts of less than 1 order of magnitude markedly affect the seepage force field and slope failure potential. Maximum effects occur if conductivity contrasts are of four orders of magnitude or more, and large hydraulic gradients commonly result in particularly large failure potentials just upslope from where low-conductivity layers intersect the ground surface.« less
  • An electrical capacitance tomography (ECT) system is used in this study to investigate the density wave generated in the gravity-driven granular flow through a vertical pipe. The experiments are conducted in two stages. First, the time-averaged quantities of particle concentration and velocity are measured and correlated with the mass flow rate of particles. Second, the power spectra of particle concentration fluctuations are examined to determine the condition for the formation of density waves. The present work finds that the time-averaged particle concentration is higher toward the centerline of the pipe and the particle velocity is relatively uniform over the crossmore » section of the pipe. The conducted load cell and fiber optic probe measurements are in reasonable agreement with the ECT measurements. The density wave formation has a close correlation with the local particle concentration. The experimental results also indicate that the dominant frequency might vary while the particle pass through the vertical pipe.« less