A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part I—Theory

Tengattini, Alessandro; Das, Arghya; Nguyen, Giang D.; Viggiani, Gioacchino; Hall, Stephen A.; Einav, Itai

doi:10.1016/j.jmps.2014.05.021

Cited by 92 publications

(58 citation statements)

References 40 publications

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“…A possible strategy to model the interaction between these two constituents is to treat the cemented granular material as a mixture of two phases subjected to the same state of deformation (i.e., ε = ε c = ε g ). As suggested by Tengattini et al , this assumption is compatible with an additive decomposition of the elastic energy stored in the two units. As a result, the overall Helmholtz free energy stored in the REV can be expressed as a volume average of individual contributions from cement and skeleton, as follows:

Ψ_{S} = φ_{g} Ψ_{M}^{g} + φ_{c} Ψ_{M}^{c}

where the term

Ψ_{M}^{g}

and

Ψ_{M}^{c}

represents the average stored energy per unit volume within the grain and cement fractions, respectively.…”

Section: Chemomechanics Of Breakage/damage In Reactive Granular Mediasupporting

confidence: 52%

“…Similar quantities are also required to track the effect of irreversible mechanical processes, for example, by defining inelastic state variables related to microscopic dissipative processes. The Breakage Mechanics theory satisfies this requirement by relating its internal variables to the evolution of the probability density function of the microstructural units of a cemented granular system (i.e., grains and cement bonds). Such units are assumed to evolve from an initial to an ultimate condition as a function of two dissipative variables referred to as Breakage, B , and Damage, D , as follows:

g^{g} ((),, x_{g}, B) = g_{0}^{g} ((), x_{g}) ((), 1 - B) + g_{u}^{g} ((), x_{g}) B

g^{c} ((),, x_{c}, D) = g_{0}^{c} ((), x_{c}) ((), 1 - D) + g_{u}^{c} ((), x_{c}) D

where x g and x c are grain and bond diameter, respectively, while g g ( x g , B ) and g c ( x c , D ) are the current grain and cement bond size probability density functions.…”

Section: Pore‐scale Idealization Of Mass Removal and Accumulationmentioning

confidence: 99%

“…Graphical interpretation of the relation between the dissipative internal variables and the evolving probability density of grain size and cement‐bond size: (a) Breakage, B and (b) Damage, D .…”

Section: Pore‐scale Idealization Of Mass Removal and Accumulationmentioning

confidence: 99%

“…As proposed by Tengattini et al , such logic can also be used for cemented granular materials by means of similar homogenization schemes and energy scaling hypotheses. As a result, the homogenized form of Helmholtz free energy for the cement phase can be expressed as follows:

Ψ_{M}^{c} ((),,, ε, D, X_{p}) = true {true\int}_{x_{c m} (X_{p})}^{x_{c M} (X_{p})} ψ_{M}^{c} ((), ε) g_{c} ((), x_{c}, D, X_{p}) normald x_{c}

…”

Section: Chemomechanics Of Breakage/damage In Reactive Granular Mediamentioning

confidence: 99%

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Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

Buscarnera

Das

2015

Num Anal Meth Geomechanics

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Summary This paper studies the chemo‐mechanics of cemented granular solids in the context of continuum thermodynamics for fluid‐saturated porous media. For this purpose, an existing constitutive model formulated in the frame of the Breakage Mechanics theory is augmented to cope with reactive processes. Chemical state variables accounting for the reactions between the solid constituents and the solutes in the pore fluid are introduced to enrich the interactions among the microstructural units simulated by the model (i.e., grains and cement bonds). Two different reactive processes are studied (i.e., grain dissolution and cement precipitation), using the chemical variables to describe the progression of the reactions and track changes in the size of grains and bonds. Finally, a homogenization strategy is used to derive the energy potentials of the solid mixture, adopting probability density functions that depend on both mechanical and chemical indices. It is shown that the connection between the statistics of the micro‐scale attributes and the continuum properties of the solid enables the mathematical capture of numerous mechanical effects of lithification and chemical deterioration, such as changes in stiffness, expansion/contraction of the elastic domain, and development of inelastic strains during reaction. In particular, the model offers an interpretation of the plastic strains generated by aggressive environments, which are here interpreted as an outcome of chemically driven debonding and comminution. As a result, the model explains widely observed macroscopic signatures of geomaterial degradation by reconciling the energetics of the deformation/reaction processes with the evolving geometry of the microstructural attributes. Copyright © 2015 John Wiley & Sons, Ltd.

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Ψ_{S} = φ_{g} Ψ_{M}^{g} + φ_{c} Ψ_{M}^{c}

where the term

Ψ_{M}^{g}

and

Ψ_{M}^{c}

represents the average stored energy per unit volume within the grain and cement fractions, respectively.…”

Section: Chemomechanics Of Breakage/damage In Reactive Granular Mediasupporting

confidence: 52%

g^{g} ((),, x_{g}, B) = g_{0}^{g} ((), x_{g}) ((), 1 - B) + g_{u}^{g} ((), x_{g}) B

g^{c} ((),, x_{c}, D) = g_{0}^{c} ((), x_{c}) ((), 1 - D) + g_{u}^{c} ((), x_{c}) D

where x g and x c are grain and bond diameter, respectively, while g g ( x g , B ) and g c ( x c , D ) are the current grain and cement bond size probability density functions.…”

Section: Pore‐scale Idealization Of Mass Removal and Accumulationmentioning

confidence: 99%

Section: Pore‐scale Idealization Of Mass Removal and Accumulationmentioning

confidence: 99%

Ψ_{M}^{c} ((),,, ε, D, X_{p}) = true {true\int}_{x_{c m} (X_{p})}^{x_{c M} (X_{p})} ψ_{M}^{c} ((), ε) g_{c} ((), x_{c}, D, X_{p}) normald x_{c}

…”

Section: Chemomechanics Of Breakage/damage In Reactive Granular Mediamentioning

confidence: 99%

See 2 more Smart Citations

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

Buscarnera

Das

2015

Num Anal Meth Geomechanics

Self Cite

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“…However, discontinuity at the grain scale, such as bond breakage, challenges continuumbased methods (Nova et al, 2003;Gao & Zhao, 2012;Tengattini et al, 2014) and highlights the merit of the distinct-element method (DEM) (e.g. Potyondy & Cundall, 2004;Jiang et al, 2007;Utili & Nova, 2008;Wang & Leung, 2008;Obermayr et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

On the size-dependent compressive resistance of bonded granules

Liu¹,

Jiang²

2015

Géotechnique Letters

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Peculiar properties of cemented geomaterials are endowed by inter-particle bonds, of which the contact behaviour has recently been found to be size dependent. This study uses the distinct-element method to investigate the size effect on the compressive resistance of an inter-particle bond, which is modelled as an assemblage of tiny bonded particles. The model parameters are carefully calibrated according to laboratory observation of a realistic reference material. The simulations demonstrate that the compressive resistance of the bond largely depends on bond slenderness and boundary curvature as well as the bond contact area. The combined effect of three size parameters can be captured in a single formula. Given the bond contact area in common, a thin bond between large particles tends to fail at higher compressive force than a thick bond between small particles because the coalescence of micro-cracks inside the bond is hindered more effectively in the thin case, resulting in ultimate failure due to compressive crushing rather than tensile cracking. A full consideration of the size effect on the bond contact strength may change the picture of progressive bond breakage in cemented geomaterials, which deserves further investigation once a size-dependent bond contact law is obtained.

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Direct observations of damage during unconfined brittle failure of Carrara marble

2016

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To observe and quantify the production of microfracturing from initial yield to failure, we deformed Carrara marble samples in uniaxial compression at 20, 105, and 180°C and continuously observed a region of about 1 mm2 on an exposed face with a long‐working distance microscope. Using image processing and microscale strain‐mapping techniques, we measured local strains over a length scale of tens of micrometers. By treating the images with various filters, we identified linear damage features, as well as the magnitude of localized strain and the mode of deformation, i.e., shear versus normal deformation. In general, shear deformation is more prevalent after initial yielding, while tensile deformation dominates closer to peak stress. Independent measurements of both stress and microcrack density at different stages of each experiment provide a unique opportunity to explicitly compare the data with damage models. The model of Ashby and Sammis (1990) significantly underestimated the damage that the rock could sustain before peak stress, perhaps owing to the influence of weak grain boundaries on the damage production. In these samples, microcracks tended to form near boundaries before yield stress. During strain hardening, the damage parameters increased rapidly as longer microcracks grew along the boundaries and finally transected grains as loading neared peak stress. The microcrack density can be empirically related to the reduction of Young's modulus; stiffness ratios decay exponentially with increasing microcrack density for T ≤ 105°C.

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A thermomechanical constitutive model for cemented granular materials with quantifiable internal variables. Part I—Theory

Cited by 92 publications

References 40 publications

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

Chemo‐mechanics of cemented granular solids subjected to precipitation and dissolution of mineral species

On the size-dependent compressive resistance of bonded granules

Direct observations of damage during unconfined brittle failure of Carrara marble

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