Analytical and Numerical Approaches to Attain the Optimum Tapering Angle for Axially-Loaded Bored Piles in Sandy Soils

Data Availability Statement

Notation

A_b

pile toe area;

A_bn

projected area of the ledge of a segment;

A_s

pile lateral surface area;

A_sn

lateral surface area of an element;

D_av

average diameter of a tapered pile;

D_b

base diameter of a tapered pile;

Dr

soil relative density;

dη

change in shear stress ratio;

$d{\epsilon }_v^p$

increment of plastic volumetric strain;

E_oed,i

Young's modulus of the interface;

G^e

elastic shear modulus;

G_i

shear modulus of the interface;

$G_i^p$

plastic modulus at a low level of stress ratio;

G^p

plastic shear modulus;

G_soil

shear modulus of the soil;

K₀

at rest lateral earth pressure coefficient;

$K_G^e$

shear modulus number that corresponds with Dr;

K_max

lateral earth pressure coefficient mobilized that correspond to maximum tapering angle;

K_p

passive earth pressure coefficient;

K_t

taper coefficient for lateral earth pressure;

k

lateral earth pressure coefficient;

k_t

taper factor for the shaft resistance of tapered pile;

L

length of pile;

N_qc

bearing capacity factor of a cylindrical pile;

N_t

bearing capacity factor for tapered piles;

P_a

atmospheric pressure;

Q_T

total bearing capacity of a single pile;

q_b

toe resistance of a single pile;

q_bt

base resistance of the tapered pile;

q_s

frictional resistance of a single pile;

q_st

shaft resistance of a single pile;

q_sv

vertical bearing resistance that stems from the body of a tapered pile;

R_f

failure ratio;

R_inter

interface coefficient;

r

radius of the pile's nth segment;

r_b

bottom radius of the pile;

r_c

radius of the counterpart same volume cylindrical pile;

r_n

radius of the nth segment;

r_t

top radius of the pile;

TF_b

taper factor for base resistance;

z

depth of the pile's nth segment;

z_mn

midelevation of the nth segment;

α

tapering angle;

α_max

maximum tapering angle for a pile with constant volume;

α_opt

optimum tapering angle;

α_r

ratio of optimum tapering angle to the maximum tapering angle;

β

correlation coefficient;

γ

soil unit weight;

γ^p

plastic shear strain increment;

δ

pile–soil interface friction angle;

ζ

correlation coefficient controls the approaching rates of assumed functions for parameters;

η

shear stress ratio;

η_f

stress ratio at failure;

λ

correlation coefficient;

μ

coefficient that corresponds to the portion of mobilized passive earth pressure coefficient;

ν_i

Poisson's ratio of the interface;

σ′

mean stress in the plane of loading;

${\sigma }_b^{\mathrm{\prime }}$

effective stresses at pile toe and midlength of the pile;

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

effective vertical stress at the middle of the nth segment;

${\sigma }_m^{\mathrm{\prime }}$

effective stresses at midlength of the pile;

τ

shear stress;

ϕ

internal friction angle of soil;

ϕ_cv

constant volume friction angle (phase transformation angle);

ϕ_i

internal friction angle of the interface; and

ψ

coefficient in bearing capacity factor suggested by Janbu that correspond to relative density.

References