Numerical and Analytical Study on Axial Ultimate Bearing Capacity of Fixed-Head Energy Piles in Different Soils

Acknowledgments

Notation

A_b

cross-sectional area of the pile;

c

soil cohesion;

C_a

adhesion between the pile and the soil;

c_o

initial value of cohesion;

C_p

specific heat of the pile material;

C_pd

specific heat of the dry soil;

C_ps

specific heat of the saturated soil;

c_s, c_p

empirical coefficients;

D

pile diameter;

E_p

modulus of elasticity of the pile material;

E_s

modulus of elasticity of the soil;

F

force inside the equivalent spring;

F_y

yield surface function of the Mohr–Coulomb model;

G_P

plastic potential function;

I_w

influence factor;

k

equivalent stiffness of the soil;

k_s

coefficient of lateral soil pressure;

k_sn

side normal stiffness of the soil;

k_ss

side tangential stiffness of the soil;

k_tn

tip normal stiffness of the soil;

L

pile length;

N_c, N_q, N_γ

bearing capacity factors;

P

perimeter of the pile;

p

mean stress value;

p_(T)

penalty factor;

P_bu

ultimate pile tip resistance;

p_o

penalty factor in the absence of the thermal radial deformation of the pile;

P_su

ultimate pile shaft resistance;

P_u

ultimate bearing capacity of an energy piles;

P_uo

ultimate bearing capacity under zero thermal interactions;

q

deviator stress;

q_ave

average value of the data observed in the experimental dataset;

q_exp

experimental observed value;

q_exp,max

maximum value of the data observed in the experimental dataset;

q_exp,min

minimum value of the data observed in the experimental dataset;

q_num

numerical result value;

R

pile radius;

R_mc

shape of the yield surface in deviator plane;

R_mw

shape parameter to define the plastic potential surface;

T_o

initial temperature;

W

pile weight;

Δ_o

axial thermal deformation along the pile axis;

Δ_b

axial deformation created inside the pile;

ΔP_uT

change in ultimate bearing capacity after imposing a heat variation;

Δ_s

total axial deformation of the pile;

ΔT

variation in temperature;

$\mathrm{\Delta }{\sigma }_r^{\mathrm{\prime }}$

excess radial stress acts on the pile shaft;

α

coefficient of thermal expansion;

α_p

coefficient of thermal expansion of the pile material;

α_s

coefficient of thermal expansion of the soil;

ε

meridional eccentricity;

ϕ

internal friction angle of the soil;

ϕ_a

angle of friction between the pile and the soil;

γ

unit weight of the pile material;

γ′

submerge unit weight of the soil;

γ_d

dry unit weight of the soil;

λ

thermal conductivity of the pile material;

λ_d

thermal conductivity of dry soil;

λ_s

thermal conductivity of the saturated soil;

ν_p

Poisson’s ratio of the pile material;

ν_s

Poisson’s ratio of the soil;

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

radial stress acts on the pile shaft in absence of the thermal radial deformations;

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

vertical effective stress;

${\sigma }_{\nu b}^{\mathrm{\prime }}$

vertical effective stress at the level of the pile tip;

τ_int

shear strength of the interface elements between the pile and the soil;

τ_s

shear strength of the soil;

τ_s-def

shear strength of the soil by considering the effect of thermal radial deformation of the pile; and

ψ

dilation angle of the soil.

References