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Prediction of flow liquefaction instability of clean and silty sands

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Abstract

Adding a small amount of non-plastic silt to clean sands may lead to dramatic loss of shear strength and a noteworthy tendency toward contraction when the mechanical behavior of the mixture is compared with that of the clean host sand. Thus, simulation of the behavior of silty sands with varying fines content is still a challenging subject in geomechanics. A unified constitutive model for clean and silty sands is presented in this paper. To eliminate the factitious decrease of void ratio associated with inactive silt particles in various silty sand mixtures, the concept of equivalent void ratio is used in the model formulation instead of the global void ratio. In addition, the instantaneous soil state is expressed in terms of intergranular state parameter taking into account the combined influence of intergranular void ratio, mean principal effective stress and fines content. Then, dilatancy and plastic hardening modulus are directly linked to the intergranular state parameter. To improve the model capacity in simulation of cyclic tests, new features are added to the plastic hardening modulus. It is shown that the proposed model can reasonably reproduce the mechanical behavior as well as the onset of flow liquefaction instability of clean and silty sands using a unique set of parameters.

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Abbreviations

A :

Dilatancy parameter (Eq. 22)

B :

Model parameter (Eq. 31)

b :

Fines participation factor (Eq. 2)

c (=M e/M c):

Model parameter

c h :

Plastic hardening parameter (Eq. 23)

D pp , D pq , D qp , D qq :

See Eqs. (45)–(49)

d :

Dilatancy function (Eq. 22)

e :

Global void ratio

e*:

Equivalent intergranular void ratio (Eq. 2)

e 0 :

Critical state line parameter (Eq. 28)

e cs :

Critical state void ratio

F(e):

Shear modulus void ratio dependency function (Eq. 29)

F(e*):

Shear and bulk moduli intergranular void ratio dependency function (Eq. 35)

f :

Yield function (Eq. 16)

FC:

Fines content

FCth :

Threshold fines content (Eq. 1)

G :

Elastic shear modulus

\( \bar{G} \) :

Gibbs free energy parameter (Eqs. 33–35)

G 0 :

Elastic shear modulus parameter (Eqs. 29, 35)

H(L):

Heaviside step function

\( H(\rho ,\bar{\rho }) \) :

See Eq. (24)

h 0 :

Plastic hardening parameter (Eq. 23)

J :

Elastic volumetric–shear coupling modulus

K :

Elastic bulk modulus

\( \bar{K} \) :

Gibbs free energy parameter (Eqs. 33–35)

K p :

Plastic hardening modulus

K p-cr :

Critical plastic hardening modulus (Eq. 53)

m :

Yield function opening parameter (Eq. 17)

M :

Critical state stress ratio

M c :

Critical state stress ratio of triaxial compression

M e :

Critical state stress ratio of triaxial extension

n b :

Bounding back-stress ratio parameter (Eq. 26)

n d :

Dilation back-stress ratio parameter (Eq. 26)

L :

Loading index

p :

Mean principal effective stress

p 0 :

Initial value of p at zero elastic strains (Eq. 33)

p ref :

Reference pressure (=100 kPa in this paper)

q :

Shear stress

q 0 :

Initial value of q at zero elastic strains (Eq. 33)

s :

See Eq. (17) for definition

Z (=D 10/d 50):

Size ratio

α :

Back-stress ratio

α in :

Initial value of back-stress ratio in the most recent shear loading (see Eq. 23)

α b :

Bounding back-stress ratio (Eq. 22)

α d :

Dilation back-stress ratio (Eq. 22)

α m :

Memory back-stress ratio (Table 2)

Γ:

Gibbs free energy function

γ :

Shear strain (Fig. 3)

χ :

Shear and bulk moduli pressure dependency exponent (see Fig. 3 and Eqs. 29, 34 and 35)

χ max :

Maximum value of χ

χ min :

Minimum value of χ

ε :

Strain tensor (see Table 1)

ε e :

Elastic strain tensor (see Table 1)

ε er :

Reversible elastic strain tensor (see Table 1)

ε ei :

Irreversible elastic strain tensor (see Table 1)

ε i :

Irreversible strain tensor (see Table 1)

ε p :

Irreversible plastic strain tensor (see Table 1)

λ :

Critical state line parameter (Eq. 28)

ξ :

Critical state line parameter (Eq. 28)

\( \rho ,\,\bar{\rho } \) :

See Eq. (25)

ε q :

Shear strain

ε v :

Volumetric strain

ϖ :

Elastic–plastic coupling variable

η (=q/p):

Stress ratio

η in :

Initial value of η at zero elastic strains (Eq. 36)

η peak :

Peak stress ratio

η PT :

Phase transformation stress ratio

ψ*:

Intergranular state parameter (Eq. 27)

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    Ali Lashkari

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Lashkari, A. Prediction of flow liquefaction instability of clean and silty sands. Acta Geotech. 11, 987–1014 (2016). https://doi.org/10.1007/s11440-015-0413-9

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