A Fully Coupled Numerical Framework for Predicting Dynamic Behavior in Unsaturated Soils and Its Application to Embankment Seismic Analysis

Data Availability Statement

Acknowledgments

Notation

b_i

body force;

b_r

parameter of anisotropy;

c₁

fitting parameter shaping the drying boundary curve;

c₂

fitting parameter shaping the wetting boundary curve;

c₃

fitting parameter shaping the scanning curve;

$D_{ijkl}^{}$

stiffness tensor;

$E_{ijkl}^{}$

stiffness tensor in Hooke’s law;

$E_{ij}^{\mathrm{RFS}}$

stiffness tensor related to the degree of saturation;

$E_{ijkl}^{ep}$

elastoplastic stiffness tensor;

e

void ratio;

f

yield surface;

κ

swelling index;

$K^{\alpha }$

bulk modulus of water/air (α = w, a);

$k^{\alpha }$

intrinsic permeability of water/air (α = w, a);

$k_{s1}^s$

initial stiffness of the scanning curve;

M

stress ratio at the critical state;

m*

parameter related to structure;

m

parameter related to overconsolidation;

N

void ratio at NCL under reference state;

N(S_r)

void ratio at NCLS under reference state;

n

soil porosity;

p

mean stress on the subloading yield surface;

$\overline{p}$

mean stress on the superloading yield surface;

$p^{\ast }$

mean stress on the normal yield surface;

p₀

mean stress under the reference state;

p_r

referenced mean stress;

Q_i

interaction between the soil and air;

q

deviatoric stress on the subloading yield surface;

$\overline{q}$

deviatoric stress on the superloading yield surface;

$q^{\ast }$

deviatoric stress on the normal yield surface;

q₀

deviatoric stress under the reference state;

R_i

interaction between the soil and water;

S_ij

deviatoric stress tensor;

S_r

degree of saturation;

$S_r^r$

residual degree of saturation;

$S_r^s$

saturated degree of saturation;

s

suction;

s_d

SWCC parameter for the AEV on the drying boundary curve;

s_w

SWCC parameter for the AEV on the wetting boundary curve;

u_a

pore air pressure;

u_w

pore water pressure;

V

integration domain in finite-element method;

v

Poisson’s ratio;

β

stress-induced anisotropic stress tensor;

δ

Kronecker’s delta;

η

stress ratio;

$\tilde{\eta }$

stress tensor related to anisotropy;

λ

compression index;

ρ

average density of the mixture;

${\rho }^{\alpha }$

intrinsic density of soil/water/air (α = s, w, a);

${\overline{\rho }}^{\alpha }$

partial density of soil/water/air (α = s, w, a);

σ_ij

total stress tensor;

${\sigma }_{ij}^{\mathrm{\prime }}$

soil skeleton stress tensor; and

ζ

magnitude of anisotropy.

References