Abstract

The Janssen effect describes the increase in pressure with depth in granular materials. However, the original Janssen formulation treats the density as constant. In this work, we examine parametric density models that depend on both pressure and moisture content and allow for temperature dependence to be easily included. We focus on physically-motivated empirical models that are built on power-law terms. These power-law terms correspond to thermodynamic equations of state, such as the ideal gas law, and polytropic processes. When coupled with the Janssen ordinary differential equation (ODE), these power-law models have the form of a Chini ODE. We study the properties of the Chini ODE for both constant and variable coefficients. We review Chini’s method for transforming these equations into separable forms and the conditions under which this approach fails. We derive a variety of novel expressions, including a critical value for the vertical-to-horizontal stress ratio which varies with depth.

Document Type

Article

Publication Date

3-2024

Notes/Citation Information

0032-5910/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc-nd/4.0/).

Digital Object Identifier (DOI)

https://doi.org/10.1016/j.powtec.2024.119493

Funding Information

Thanks to Eric Hawley, Sandeep Thakur, Joel Smid, Sristi Mund- hada, Zeel Khokhariya, Michael Sama and Barry Farmer for many inter- esting discussions. We would also like to thank our anonymous referees for refining the focus of this work. A. R. thanks Andrew Senchuk for insightful discussions on numerical methods. G.D. thanks the University of Manitoba for support through the Graduate Fellowship (UMGF) as well as support through the MITACS program.

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