A Nonlinear Softening Load-Transfer Approach for the Thermomechanical Analysis of Energy Piles

Acknowledgments

Notation

A_i

area of the pile cross section;

a, b, c

coefficients of the GNS model;

c′

effective cohesion;

D

pile diameter;

E

Young’s modulus of the pile;

F_u

unbalanced force;

f, g

parameters of the hyperbolic model;

f_s(s_s,M)

load-transfer function of the skin resistance of the pile;

G_b

shear modulus of the soil at the pile tip;

N_q, N_c

load capacity coefficients;

P_u

axial capacity of the pile;

Q_b,MT, Q_t,MT

thermomechanical forces at the top and base of the pile element;

$Q_{s,MT}^j$

shaft resistances of the pile element;

Q_t,M, Q_b,M, Q_s,M

axial force at the top, base, and middle of the pile element;

q_b

tip reaction;

q_bu

ultimate pile tip reaction;

q_bur

unloading or reloading tip reaction;

R_bf

pile tip resistance damage ratio;

$s_{t,MT}^i$, $s_{b,MT}^i$

thermomechanical displacements at the top and base of the pile element;

α_T

thermal expansion coefficient of the pile;

β_s

ratio of the residual interface strength to the ultimate skin friction;

Δ_b

displacement of the pile tip;

Δ_s(z)

shear displacement of the pile–soil interface at a given pile depth;

ΔT

temperature change of the pile;

${\mathrm{\Delta }}_T^i$

thermal deformation of the pile;

Δ_u

critical displacement;

Δ₀(z)

skin friction at the initial states of the unloading and reloading;

Δ₀, q_b0

initial states of unloading and reloading, respectively;

δ

friction angle of the pile–soil interface;

η

judgment factor of the loading condition;

μ

empirical coefficient;

ν

Poisson's ratio of the soil at the pile tip;

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

pile tip vertical stress;

σ_z

effective overburden pressure;

τ_s(z)

skin friction at a given pile depth;

τ_sr

ratio of the residual interface strength;

τ_u

ultimate skin friction;

τ_ur(z)

unloading or reloading skin resistance;

τ₀(z)

skin friction t at the initial states of the unloading and reloading;

φ′

effective friction angle of the pile tip soil; and

φ_s

soil friction angle.

References