Prediction of Pile Response in Lateral Spreading Soil Using Multigene Genetic Programming

Acknowledgments

Notation

a_max

amplitude of input motion;

a₀, a₁, a₂

coefficients of the MGGP model;

D

diameter of pile;

d

pressure-dependent constant for the PDMY02 model;

Dr_L

relative density of liquefiable layer;

Dr_NL

relative density of surface crust;

E_p

elastic modulus of pile;

E_s

elastic modulus of soil;

f

frequency of input motion;

G

instantaneous soil shear modulus;

G_r

soil shear modulus at reference effective confining pressure;

H_L

thickness of liquefiable layer;

H_NL

thickness of surface crust;

k

fractional index;

k_i, k_b, k_l, k_d

permeability of sand during initial, buildup, liquefaction, and dissipation phase;

K_HH

lateral stiffness of pile;

L

length of pile;

m

number of data points;

M_max

maximum bending moment;

N

number of significant cycles;

N_f

number of trails exceeding the failure criterion;

N_r

number of parameters for reliability assessment;

n

number of parameters;

n₁, n₂

number of data points of training and testing tests;

p

percentage difference in pile response;

p′

effective confining pressure;

$p_r^{\mathrm{\prime }}$

reference effective confining pressure;

R²

coefficient of determination;

r_u

excess pore pressure ratio;

S

slope of ground;

T₁, T₂, T₃, T₄, T₅, T₆, T₇, T₈, T₉

genes;

x_i, z_i

numerical and predicted ith response values;

β₀, β_i, β_ii, β_ij

coefficients of second-order model;

δ_phd

maximum pile head displacement;

θ

angle of batter;

λ, β₁, β₂

variable permeability function coefficients;

μ₁, μ₂

mean of training and testing sets;

σ

standard deviation; and

ω₁, ω₂

variance of training and testing sets.

References