Numerical Investigation of Concrete Cracking Effect on Lateral Load Response of Piles in Rock Mass

Data Availability Statement

Notation

A_c

compression area of concrete;

A_el

size of the finite element;

A_fi

area of steel bar row;

a, m_b, m_i, s

constants of the Hoek–Brown failure criterion;

D

disturbance factor;

d

pile diameter;

E_c

Young’s modulus of concrete;

E_i

intact rock modulus;

E_m

rock mass deformation modulus;

EI

flexural rigidity;

EI_cr

cracked flexural rigidity;

EI_e

effective flexural rigidity;

EI_g

uncracked flexural rigidity (gross flexural rigidity);

F

yield function;

F_c

force in concrete;

FEA_NN

finite-element analysis considering nonlinear rock and pile behavior;

FEA_NL

finite-element analysis considering nonlinear rock and linear pile behavior;

F_s

force in steel;

f_c

compressive strength of concrete;

f_cfn

normalized compressive failure strength;

f_con

normalized initial compressive yield stress;

f_cun

normalized residual compressive strength;

f_cy

uniaxial compressive yield stress;

f_t

tensile yield stress;

f_tun

normalized residual tensile strength;

f_ty

uniaxial tensile yield stress;

f_y

yield strength of steel;

f_t

tensile strength of concrete;

G_c

compressive fracture energy of concrete;

G_t

tensile fracture energy of concrete;

H_c

normalized hardening/softening parameter;

h_i

distance from the neutral axis to the middle of the strip;

I_eff

effective moment of inertia;

I_g

moment of inertia of the gross section;

L

pile length;

L_eq

characteristic length of the finite element;

L_i

strip length;

M

applied bending moment;

M_cr

cracking moment;

n

number of steel bars in each row;

n_f

modulus to the concrete Young’s modulus;

n_GP

number of stress points per element;

P

lateral load;

r

pile radius;

x_i

distance from the neutral axis position to the steel bars row;

y

deflection of the pile;

y_c

position of the neutral axis;

y′

compression area to the centroid of the pile;

z

depth;

z_i

distance to top compression fiber for each steel bars row at level i;

γ′

effective unit weight of rock mass;

σ₁

major principal stresses;

σ₃

minor principal stresses;

σ_c

concrete stress;

σ_ci

unconfined compressive strength of the intact rock;

σ_rot

failure envelope and the horizontal axis;

σ_s

steel stress;

Δh_i

strip width;

${\epsilon }_1^p$

major plastic strain;

${\epsilon }_3^p$

minor plastic strain;

${\epsilon }_{\mathrm{cp}}^p$

plastic peak strain;

${\epsilon }_{\mathrm{tu}}^p$

plastic ultimate strain (uniaxial tension test);

ɛ_c

concrete strain;

ɛ_o

compressive strain at peak compressive stress;

ɛ_s

steel strain;

ɛ_y

steel strain at yield strength;

ν

Poisson’s ratio;

ψ

dilatancy angle of concrete;

φ_max

friction angle of concrete; and

к

curvature.

References