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Criterion for flow liquefaction instability

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Abstract

This study describes a general liquefaction flow instability criterion for elastoplastic soils based on the concept of loss of uniqueness. We apply the criterion to the general case of axisymmetric loading and invoke the concepts of effective stresses and loss of controllability to arrive at a general criterion for the onset of liquefaction flow. The criterion is used in conjunction with an elastoplastic model for sands to generate numerical simulations. The numerical results are compared with experimental evidence to give the following insights into predicting liquefaction. (1) The onset of liquefaction flow is a state of instability occurring under both monotonic and cyclic tests, and coincides with loss of controllability. (2) The criterion proposed herein clearly and naturally differentiates between liquefaction flow (instability) and cyclic mobility. (3) Flow liquefaction not only depends on the potential of the material to generate positive excess pore pressures, but more importantly, it also depends on the current state of the material, which is rarely predicted by phenomenology.

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Abbreviations

A 0 :

Material constant in Dafalias Manzari model

A d :

Positive scaling function of dilatancy

c h :

Material constant in Dafalias Manzari model

d 2 W :

Second-order work per unit volume

e :

Current void ratio

e c :

Void ratio on critical state line

e 0 :

Initial void ratio

e c0 :

Critical state line material constant

F :

Yield surface

G :

Shear modulus

G 0 :

Elastic shear modulus

H :

Hardening modulus

H L :

Critical hardening modulus

h :

Positive state variable in Dafalias Manzari model

h 0 :

Material constant in Dafalias Manzari model

K :

Bulk modulus

M :

Critical stress ratio

m :

Material constant in Dafalias Manzari model

M b :

Bounding stress ratio

M d :

Dilatancy stress ratio

n b :

Material constant in Dafalias Manzari model

n d :

Material constant in Dafalias Manzari model

η in :

Initial value of η at initiation of a new loading process

p :

Volumetric stress

\( \dot{p} \) :

Volumetric stress rate

P at :

Atmospheric pressure

Q :

Plastic potential

q :

Deviatoric stress

\( \dot{q} \) :

Deviatoric stress rate

z :

Fabric dilatancy factor

z max :

Material constant in Dafalias Manzari model

α :

Back stress ratio

\( \dot{\alpha } \) :

Evolution law for back stress

β :

Dilatancy

\( \dot{\boldsymbol{\epsilon}} \) :

Strain vector increment

\( \dot{\epsilon}_{\text{a}} \) :

Axial strain rate

\( \dot{\epsilon}_{\text{r}} \) :

Radial strain rate

\( \dot{\epsilon }_{\text{s}} \) :

Total deviatoric strain rate

\( \dot{\epsilon}_{\text{s}}^{\text{e}} \) :

Elastic deviatoric strain rate

\( \dot{\epsilon}_{\text{s}}^{\text{p}} \) :

Plastic deviatoric strain rate

\( \dot{\epsilon}_{\text{v}} \) :

Total volumetric strain rate

\( \dot{\epsilon}_{\text{v}}^{\text{e}} \) :

Elastic volumetric strain rate

\( \dot{\epsilon}_{\text{v}}^{\text{p}} \) :

Plastic volumetric strain rate

η :

Stress ratio

v :

Poisson’s ratio

ψ:

State parameter

λ c :

Critical state line material constant

σ a :

Axial stress

σ r :

Radial stress

\( \dot{\sigma }_{\text{a}} \) :

Axial stress rate

\( \dot{\sigma }_{\text{r}} \) :

Radial stress rate

ξ:

Critical state line material constant

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Acknowledgments

AMR acknowledges the financial support given to this work by Pontificia Universidad Javeriana by grant number 004705 'Numerical and experimental research of diffuse instability in granular matter.' Support for JEA’s work was partially provided by NSF grant number CMMI-1060087. This support is gratefully acknowledged. The authors thank Ivan Vlahinic and Utkarsh Mital from Caltech for proofreading this manuscript.

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Authors and Affiliations

  1. Civil and Mechanical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, USA

    José E. Andrade

  2. Geophysical Institute, Pontificia Universidad Javeriana, Cra 7 No 42-27, Bogotá, Colombia

    Alfonso M. Ramos

  3. SRK Consulting, 1066 West Hastings St., Vancouver, V6E 3X2, Canada

    Arcesio Lizcano

Authors
  1. José E. Andrade
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  2. Alfonso M. Ramos
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  3. Arcesio Lizcano
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Correspondence to José E. Andrade.

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Andrade, J.E., Ramos, A.M. & Lizcano, A. Criterion for flow liquefaction instability. Acta Geotech. 8, 525–535 (2013). https://doi.org/10.1007/s11440-013-0223-x

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