A Constitutive Model with a Historiotropic Yield Surface for Sands

Tavera, Carlos Eduardo Grandas; Triantafyllidis, Theodoros; Knittel, Lukas

doi:10.1007/978-3-030-28516-6_2

Cited by 6 publications

(23 citation statements)

References 18 publications

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“…Its size in the effective stress space is described by the scalar state variable

p_B

, defining the isotropic part of the back stress tensor

{\bm \sigma }_B

and the inclination of its bisector with the deviatoric structural tensor Ω defining the deviatoric part of

{\bm \sigma }_B

\begin{equation} {\bm \sigma }_B=p_B{\left(-\mathbf {1}+\bm{\Omega }\right)}. \end{equation}

The proposed flow surface is similar to the one proposed in Grandas‐Tavera et al 50 . for sand and reads:

\begin{equation} F({\bm \sigma },{\bm \sigma }_B)=\rm w:\rm w-\dfrac{2}{3}M_{\rm w}^{2}\underbrace{{\left[1-{\left(\dfrac{p^{\prime }}{p_B}\right)}^{c_B}\right]}}_{D} \underbrace{{\left[1-\sqrt {\dfrac{3}{2}}\dfrac{\sqrt {\bm{\Omega }:\bm{\Omega }}}{M_{\bm{\Omega }}}\right]}^2}_{G} \end{equation}

whereby

\rm w

is a deviatoric tensor capturing the position of the current stress with respect to the major axis of the flow surface:

boldw badbreak= \overset{̂<...}{bold-italicσ}

…”

Section: Historiotropic Flow Surfacementioning

confidence: 99%

“…The adopted dilatancy description (Equations (47)–(49)) was established in Tafili et al 59 . according to extensive experimental evidence on fine‐grained soils 7,10,11,50 and the attentive reader is referred to these works for comprehensive details.…”

Section: Mechanical Model Formulationmentioning

confidence: 99%

“…Figure 12 contains the characteristic friction angles

\varphi _c

\varphi _{peak}

and

\varphi _{ptl}

as functions of the normalized void ratio

e/e_c

for Kaolin and for a sand provided in Grandas‐Tavera et al 50 . Notice the different values of this parameter for clays in comparison to sands

n_{peak}=2

50 . Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well.…”

Section: Calibration Of Materials Parametersmentioning

confidence: 99%

“…Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well.

\varphi _p

of clays has a vertex and varies exponentially between

e/e_c=

0.8 and 1.2, whereas

\varphi _p

of sands 50 is almost a linear function of

e/e_c

in the range between 0.8 and 1.4.…”

Section: Calibration Of Materials Parametersmentioning

confidence: 99%

“…The model has been proposed for viscous and non‐viscous clays, but it is not limited only to fine‐grained soils. Moreover, Grandas et al 50 . proposed a model using similar tools to describe the behaviour of sands.…”

Section: Final Remarksmentioning

confidence: 99%

See 4 more Smart Citations

Constitutive anamnesis model (CAM) for fine‐grained soils

Tafili

Grandas

Triantafyllidis

et al. 2022

Num Anal Meth Geomechanics

Self Cite

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Mainly, two divisions are encountered in the literature regarding constitutive models: elasto-plasticity and hypoplasticity. In addition, barodesy and the framework of generalized plasticity are used. The main disadvantage of nearly all models is the failure to reproduce the mechanical behaviour under cyclic loading without restrictions. A model which deals neither with the true hypoplastic nor the true elasto-plastic approach will be proposed herein. Moreover, it combines and establishes the unification of both frameworks and it can be assigned to both of them. It introduces a so called historiotropic surface, responsible for the memory of the soil, but no consistency condition. It also introduces a hypoplastic strain rate, but incorporating the distance to the new surface for its intensity and the back stress tensor. Hence, both the intergranular strain as well as the fabricdilatancy tensor are omitted, even though the eight-shaped stress hysteresis at cyclic mobility is well reproduced.

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“…Its size in the effective stress space is described by the scalar state variable

p_B

, defining the isotropic part of the back stress tensor

{\bm \sigma }_B

and the inclination of its bisector with the deviatoric structural tensor Ω defining the deviatoric part of

{\bm \sigma }_B

\begin{equation} {\bm \sigma }_B=p_B{\left(-\mathbf {1}+\bm{\Omega }\right)}. \end{equation}

The proposed flow surface is similar to the one proposed in Grandas‐Tavera et al 50 . for sand and reads:

\begin{equation} F({\bm \sigma },{\bm \sigma }_B)=\rm w:\rm w-\dfrac{2}{3}M_{\rm w}^{2}\underbrace{{\left[1-{\left(\dfrac{p^{\prime }}{p_B}\right)}^{c_B}\right]}}_{D} \underbrace{{\left[1-\sqrt {\dfrac{3}{2}}\dfrac{\sqrt {\bm{\Omega }:\bm{\Omega }}}{M_{\bm{\Omega }}}\right]}^2}_{G} \end{equation}

whereby

\rm w

is a deviatoric tensor capturing the position of the current stress with respect to the major axis of the flow surface:

boldw badbreak= \overset{̂<...}{bold-italicσ}

…”

Section: Historiotropic Flow Surfacementioning

confidence: 99%

Section: Mechanical Model Formulationmentioning

confidence: 99%

“…Figure 12 contains the characteristic friction angles

\varphi _c

\varphi _{peak}

and

\varphi _{ptl}

as functions of the normalized void ratio

e/e_c

for Kaolin and for a sand provided in Grandas‐Tavera et al 50 . Notice the different values of this parameter for clays in comparison to sands

n_{peak}=2

50 . Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well.…”

Section: Calibration Of Materials Parametersmentioning

confidence: 99%

“…Figure 12 shows the difference in the shape of the peak friction angle of sands and clays as well.

\varphi _p

of clays has a vertex and varies exponentially between

e/e_c=

0.8 and 1.2, whereas

\varphi _p

of sands 50 is almost a linear function of

e/e_c

in the range between 0.8 and 1.4.…”

Section: Calibration Of Materials Parametersmentioning

confidence: 99%

Section: Final Remarksmentioning

confidence: 99%

See 3 more Smart Citations

Constitutive anamnesis model (CAM) for fine‐grained soils

Tafili

Grandas

Triantafyllidis

et al. 2022

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

show abstract

Neohypoplasticity Revisited

Mugele,

Niemunis,

Stutz

2023

Num Anal Meth Geomechanics

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This paper presents further improvements to the neohypoplasticity (NHP), a constitutive model for sand, which overcomes some shortcomings of widely used hypoplastic models. The novelties presented in this paper includes a new description of the additional dilatancy due to the structural variable and the introduction of a new state variable, denoted as , to consider the small strain stiffness in case of a 1D loading reversal. They remove shortcomings of earlier versions of NHP. The new formulations are presented and the performance of NHP is validated with experimental data from Karlsruhe fine sand. Both monotonic and cyclic tests are simulated under drained and undrained conditions. The results demonstrate that the NHP accurately reproduces the observed behaviour in monotonic and cyclic experiments.

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New perspectives on preshearing history in granular soils

Knittel¹,

Tafili

Tavera

et al. 2023

Sci Rep

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The design of deep dump slopes for opencast mines usually requires information about the soil resistance to liquefaction during earthquakes. This resistance depends not only on the initial stress, the initial density, and the amplitude of the cyclic loading, but also on the preshearing, that is, the deviatoric stress path applied to the soil before the cyclic loading. To explore the influence of preshearing on the subsequent soil behaviour, a set of triaxial tests with a combination of undrained preshearing and drained stress cycles using two sample preparation methods is presented. It is shown that the preshearing as well as the preparation method have a major influence on the strain accumulation upon cyclic loading. Simulations of the experiments with four advanced constitutive models reveal that neither the long-lasting effect of preshearing nor the preparation method can adequately be captured by all of the models. This deficiency of the constitutive models can lead to unsafe designs due to the overestimation of the cyclic resistance to liquefaction and to the underestimation of long term settlements.

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A Constitutive Model with a Historiotropic Yield Surface for Sands

Cited by 6 publications

References 18 publications

Constitutive anamnesis model (CAM) for fine‐grained soils

Constitutive anamnesis model (CAM) for fine‐grained soils

Neohypoplasticity Revisited

New perspectives on preshearing history in granular soils

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