Application of an Optimization Algorithm for Calibrating Soil Bounding Surface Plasticity Models for Cyclic Loading

Conclusions

Data Availability Statement

Acknowledgments

Notation

A₀ and n^d

dilatancy parameters;

a_d

damage parameter for SANICLAY-B;

C

parameter that governs the rate of rotational hardening;

c, λ_c, e₀, and ξ

critical-state parameters;

c_d

damage parameter for SANICLAY-H;

d

dilatancy parameter;

e

void ratio;

e_g, A_g, n_g

fitting parameters for the maximum shear modulus;

e₀

initial void ratio;

G₀

elasticity constants;

H

plastic modulus;

h_c

parameter that adjusts the magnitude of the plastic modulus under compression in SANICLAY-H;

h_e

parameter that adjusts the magnitude of the plastic modulus under extension in SANICLAY-H;

h₀

parameter that adjusts the magnitude of the plastic modulus in SANICLAY-B;

I_W

identity matrix with different dimensions to ${\mathit{I}}_{\theta }$;

${\mathit{I}}_{\theta }$

identity matrix;

i

iteration number index;

J

Jacobian matrix;

k_i

destructuration parameter;

L

plastic multiplier (loading index);

M_c

critical state ratio under compression;

M^d

dilatancy line;

M_e

critical state ratio under extension;

m

yield surface parameter;

N

total number of model parameters;

N

variable limiting the rotation of the bounding surface;

p

mean effective stress;

p_at

atmospheric pressure;

$(\overline{p},\overline{q})$

image stress;

(p_c, q_c)

projection center;

p₀

initial confining stress;

p₀

isotropic hardening variable;

$p_{\alpha }$

dummy variable to adjust the size of the plastic potential;

q

deviatoric stress;

$R_d^i$

flow direction of the deviatoric strain;

$R_v^i$

flow direction of the volumetric strain;

r(θ)

residual vector;

S

total number of data points;

u

pore water pressure;

W

diagonal weight matrix;

w′

vector of the data points’ weight;

x

parameter limiting the upper bound rotation of the bounding surface;

y_exp

vector of target data;

y(θ)

vector of simulation results;

z

fabric parameter;

z_max and c_z

fabric dilatancy tensor parameters;

α

back-stress ratio;

α

rotational hardening variable;

α^b

bounding (limiting) value of α;

γ

shear strain;

γ_0.7

parameter of elastic stiffness degradation rate;

δθ

small perturbations in input parameters;

ɛ_a

axial cyclic strain amplitude;

ɛ_q

deviatoric strain;

$\overline{\eta }$

image stress ratio;

θ

vector of input parameters;

κ

slope of the recompression line in the e − ln(p) space;

λ

slope of the virgin compression line in the e − ln(p) space;

λ

Levenberg–Marquardt damping parameter;

${\sigma }_{\mathit{v}\mathit{c}}^{\mathrm{\prime }}$

vertical consolidation stress;

ν

Poisson's ratio;

ψ

state parameter;

ω

hybrid flow rule parameter; and

〈 〉

Macaulay brackets.

References