Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA multiphase constitutive modeling framework for unsaturated soil behavior
139
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We develop a framework for constitutive modeling of unsaturated soils that has the embedded elements of lower scale grain to grain contacts. Continuum models developed from this framework will possess two different phases idealizing the solid grains and their interactions. As a consequence, two different constitutive relationships, corresponding to the grain to grain contact and bulk behavior, co-exist in a constitutive model and govern the response of the model. To be specific, grain to grain sliding under dry or wet condition is idealized and appears as a simple contact law embedded in a continuum framework. There is no need to define plastic strain, as this quantity naturally emerges at the continuum scale as the consequence of frictional sliding at the lower scale. In addition, the effective stress can be naturally worked out from the grain to grain contact law embedded in the model without being subjected to any interpretation. This, in our opinion, is a closer representation of unsaturated soil behavior, compared to existing continuum approaches that map everything onto a single stress-strain relationship. In this paper, the framework is presented in its simplest form that takes into account sliding on a single orientation. Grain to grain contact law with capillary effects is used for the demonstration of the concept, and the technical details behind it. Generalization of the framework for better representation of unsaturated soil behavior will also be sketched out.
rate research
Read More
We present a reformulation of the reactive rod model (RRM) of Dutta and Graham [Dutta, Sarit and Graham, Michael D., JNNFM 251 (2018)], a constitutive model for describing the behavior of dilute wormlike micelle solutions. The RRM treats wormlike micelle solutions as dilute suspensions of rigid Brownian rods undergoing reversible scission and growth in flow. Evolution equations for micelle orientation and stress contribution are coupled to a kinetic reaction equation for a collective micelle length, producing dynamic variations in the length and rotational diffusivity of the rods. This model has previously shown success in capturing many critical steady-state rheological features of dilute wormlike micelle solutions, particularly shear-thickening and -thinning, non-zero normal stress differences, and a reentrant shear stress-shear rate curve, and could fit a variety of steady state experimental data. The present work improves on this framework, which showed difficulty in capturing transient dynamics and high-shear behavior, by reformulating the kinetic equation for micelle growth on a more microstructural (though still highly idealized) basis. In particular, we allow for micelle growth associated with strong alignment of rods and breakage due to tensile stresses along the micelles. This new formulation captures both steady and transient shear rheology in good agreement with experiments. We also find good agreement with available steady state extensional rheology.
Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $phi$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $phi$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(phi,tilde{sigma}$, and $mu)$, with $tilde{sigma} = sigma/sigma_0$ the dimensionless shear stress and $mu$ the coefficient of interparticle friction: the dimensional stress is $sigma$, and $sigma_0 propto F_0/ a^2$, where $F_0$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or textquotedblleft jammingtextquotedblright points at volume fraction $phi_{rm J}^0 = phi_{rm rcp}$ (random close packing) for the low-stress lubricated state, and at $phi_{rm J} (mu) < phi_{rm J}^0$ for any nonzero $mu$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results.
Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools. We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g. type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2.
We present a new strategy for introducing population balances into full-chain constitutive models of living polymers with linear chain architectures. We provide equations to describe a range of stress relaxation processes covering both unentangled systems (Rouse-like motion) and well entangled systems (reptation, contour length fluctuations, chain retraction, and constraint release). Special attention is given to the solutions that emerge when the breaking time of the chain becomes fast compared to various stress relaxation processes. In these fast breaking limits, we reproduce previously known results (with some corrections) and also present new results for nonlinear stress relaxation dynamics. Our analysis culminates with a fully developed constitutive model for the fast breaking regime in which stress relaxation is dominated by contour length fluctuations. Linear and nonlinear rheology predictions of the model are presented and discussed.
A minimalist stochastic model of primary soil salinity is proposed, in which the rate of soil salinization is determined by the balance between dry and wet salt deposition and the intermittent leaching events caused by rainfall events. The long term probability density functions of salt mass and concentration are found by reducing the coupled soil moisture and salt mass balance equation to a single stochastic differential equation driven by multiplicative Poisson noise. The novel analytical solutions provide insight on the interplay of the main soil, plant and climate parameters responsible for long-term soil salinization. In particular, they show the existence of two distinct regimes, one where the mean salt mass remains nearly constant (or decreases) with increasing rainfall frequency, and another where mean salt content increases markedly with increasing rainfall frequency. As a result, relatively small reductions of rainfall in drier climates may entail dramatic shifts in long-term soil salinization trends, with significant consequences e.g. for climate change impacts on rain-fed agriculture.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
