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A critical state constitutive model for clean and silty sand

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Abstract

The mechanical behavior of silty sand is highly dependent on the percentage of fines in addition to the packing density and confining pressure. Properly modeling the diverse behavior of silty sand remains an area of difficulty and uncertainty. This paper presents an attempt to formulate a critical state-based constitutive model for sand with varying fines content based on several new laboratory findings. A marked feature of the model is a unified description of the state-dependent elastic modulus as well as a unified description of plastic hardening modulus such that only one set of elastic and hardening parameters is required for sand with different fines contents. The model is calibrated and validated using the results from a structured experimental program. It shows that the model can produce reasonably good predictions for undrained shear responses of sand specimens under a range of void ratios, confining stresses and fines contents. In particular, it successfully predicts the laboratory observation that under otherwise similar conditions, the presence of non-plastic fines increases the liquefaction susceptibility of sand.

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Abbreviations

A e :

Fitting parameter of G using F(e)

a e :

Fitting parameter of G in F(e)

A ψ :

Fitting parameter of G using F(ψ)

a ψ :

Fitting parameter of G in F(ψ)

C 0 :

Model parameter in Cr

C r :

Reduction factor for elastic shear modulus

D :

Dilatancy

d 0 :

Dilatancy parameter

dε q :

Deviatoric strain increment

dε eq :

Elastic deviatoric strain increment

dε pq :

Plastic deviatoric strain increment

dε v :

Volumetric strain increment

dε ev :

Elastic volumetric strain increment

dε pv :

Plastic volumetric strain increment

e :

Void ratio

e 0 :

Initial void ratio prior to shearing (i.e., post-consolidation void ratio ec)

e Γ :

Intercept of critical state line (CSL) in the e − (p′/Pa)ξ plane

F(e):

Void ratio function

f(X 1, X 2, X 3…):

Function of X1, X2, X3…

F(ψ):

State parameter function

FC:

Fines content (%)

f c :

Fines content in decimal

G :

Elastic shear modulus

h, h 1, h 2 :

Hardening parameters

K :

Elastic bulk modulus

k :

Pressure exponent of modulus

k 1 :

Model parameter in Cr

K p :

Plastic hardening modulus

L :

Loading index

m :

Dilatancy parameter

M :

Stress ratio (η) at critical state

n :

Hardening parameter

p′ :

Mean effective stress

p c ′ :

Post-consolidation pressure (i.e., initial mean effective stress)

P a :

Reference stress equaling to 1 atm

PSD:

Particle size distribution

PTS:

Phase transformation state

q :

Deviatoric stress

R :

Roundness of sand particle

R comb :

Combined roundness

UIS:

Undrained instability state

α :

Model parameter in Kp

ε q :

Deviatoric strain

ε eq :

Elastic deviatoric strain

ε pq :

Plastic deviatoric strain

ε v :

Volumetric strain

ε ev :

Elastic volumetric strain

ε pv :

Plastic volumetric strain

ζ :

Accumulated plastic deviatoric strain

η :

Stress ratio q/p′

η peak :

Stress ratio (η) at peak state

η PTS :

Stress ratio (η) at phase transformation state

λ c :

Magnitude of the slope of CSL

ν :

Poisson’s ratio

ξ :

Pressure exponent of CSL formulation

φ cs :

Critical state friction angle

ψ :

State parameter

ψ 0 :

Initial state parameter prior to shearing

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Acknowledgements

This work was supported by the Research Grants Council of Hong Kong through the General Research Fund (17250316, 17205717). This support is gratefully acknowledged.

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  1. Department of Civil Engineering, The University of Hong Kong, Hong Kong, China

    X. Wei & J. Yang

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  1. X. Wei
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Correspondence to J. Yang.

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Wei, X., Yang, J. A critical state constitutive model for clean and silty sand. Acta Geotech. 14, 329–345 (2019). https://doi.org/10.1007/s11440-018-0675-0

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