Janssen’s model

Figure 8.6. Janssen s model for stress distribution in cylindrical bins (a) Schematic of the forces applied to a differential slice (b) Wall pressure distribution Eq. (8.16).

A simple model for the estimation of stress distribution in cohesionless bulk solids stored in a tall cylindrical bin was presented by Janssen in 1895. The system of consideration is shown in Fig. 8.6(a). In Janssen s model, it is assumed that... 

It should be noted that the stresses in Janssen s model are cross-sectionally averaged. Therefore, Janssen s results in principle are not applicable for local stress analysis. This argument can be clearly shown by the inconsistency of Eqs. (8.15) and (8.16) with the equations of equilibrium. 

It has been explained previously (Figure 18.4) that the stacking of a granular material within the gravity field generates a pressure force in the Ox direction. The two stresses and ctzz are related but not necessarily equal. Janssen s model postulates a proportionality relationship between them, that is ... 

We now turn to a macroscopic description, using continuum mechanics, to describe the static equihbrium of a granular materialmedium. The forces applied in the granular material are thus modeled at a scale larger than that of a grain. This approach is disproved by detailed stodies, as shown by the results of the microscopic approach, but specialists" acknowledge that Janssen s theory (1895) satisfactorily... 

Janssen-Jurkovicova et al. (1994) presented a conceptual model for CCB weathering, which breaks the process into four phases. Figure 2 illustrates their model for weathering of alkaline fly ash (i.e., fly ash producing alkaline water extracts defined as fly ash having Ca/S > 2.5 by Ainsworth Rai 1987), modified using observations of Warren Dudas (1984). In phase 1, oxides and soluble salts present on ash particle surfaces dissolve in contact with water. Hydrolysis of metal oxides (especially CaO) results in a rapid rise of pH to values of approxi-... 

Thakali S, Allen HE, Di Toro DM, Ponizovsky AA, Rooney CP, Zhao F-J, McGrath SP, Criel P, van Eeckhout H, Janssen CR, Oorts K, Smolders E. 2006a. A terrestrial biotic ligand model. 2. Application to Ni and Cu toxicities to plants, invertebrates, and microbes in soil. Environ Sci Technol 40 7094-7100. 

Janssens I. A., Kowalski A. S., and Ceulemans R. (2001) Forest floor CO2 fluxes estimated by eddy covariance and chamber-based model. Agri. Forest Meteorol. 106(1), 61—69. 

Janssen, M.H.M. and Stolte, S. (1987) Calculation of steric effects in reactive collisions employing the angle-dependent line of centers model. J. Phys. Chem. 91, 5480-5486. 

De Schamphelaere, K.A., S. Lofts, and C.R. Janssen. 2005. BioavaUability models for predicting acute and chronic toxicity of zinc to algae, daphnids, and fish in natural surface waters. Environ. Toxicol. Chem. 24 1190-1197. 

R. A J. Janssen, in Primary Photoexdtations in Conjugated Polymers Molecular Eiutiton versus Semiconductor Band Model (N. S. Sariciftd, Ed.), pp. 524-558. World Scientific, Singapore, 1997. 

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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