Response and Stability of Piles Subjected to Excavation Loading

Data Availability Statement

Acknowledgments

Notation

d

diameter of an equivalent solid cylinder pile (L);

EI

flexural stiffness of pile (FL²);

E_p

Young's modulus of an equivalent solid, cylindrical pile (FL⁻²);

E_s

Young's modulus of sand or clay (FL⁻²);

FPUL

force per unit length (FL⁻¹);

G_s, G*

shear modulus of soil, and G* (1 + 0.75v_s)G_s (FL⁻²);

H

shear force at a depth of a or just about a sliding layer (F);

K_p

coefficient of passive earth pressure of sliding layer;

k_G, k_T, k_θ

rotational stiffness of a pile-cap (or a nonliquefied layer), a stable layer (e.g., underlying a liquefied layer), and total rotational stiffness of a pile, respectively;

k_s

modulus of subgrade reaction of the sliding layer (FL⁻²);

$k_s^{\mathrm{profile}}$

k_s deduced from response profiles (FL⁻²);

$k_{\theta }^{\ast },k_T^{\ast }$

stiffness k_θ and k_θB that cause singularity and amplified response of piles;

L_e

length of elastic, lower segment (L);

l, l_m

length of pile embedment, and thickness of final moving layer, respectively (L);

l_e

effective pile length (L);

l_exc

depth of excavation (L);

l_s

loading depth (L);

l_s

on-pile loading (slide) depth (for stepwise calculation) (L);

M(z)

bending moment at depth z (FL⁻²);

M_L

${\overline{M}}_L{p}_s{l}^2$, calculation parameter (FL⁻²);

M_m (M_o)

maximum bending moment within a pile (or at the mudline level) (FL⁻²);

m

ratio of the subgrade modulus of the stable layer k_s2 over that of the sliding layer k_s;

P

vertical load on passive piles (F);

P_h

H + l_sp_s, calculation parameter (F);

p(z), p_i(z)

net on-pile force per unit length at a depth z (FL⁻¹); on-pile force per unit length at a depth z calculated for sliding (i 1), and stable (i 2) layer, respectively using the elastic solutions (FL⁻¹);

p_s

limiting force per unit length in sliding layer due to soil movement (≥w_s* = p_s/k_s) (FL⁻¹);

p_ub (p_b)

limiting force per unit length at tip-level of a free-head pile during passive loading, and p_b αp_ub (FL⁻¹);

Q_m

maximum shear force within a pile (maximum of Q_m1 and Q_m2) (F);

Q_m1, Q_m2

peak shear force in sliding layer and stable layer, respectively (F);

Q(z)

shear force at depth z (F);

s_u

undrained shear strength of clay (FL⁻²);

w_g

pile displacement at GL (L);

w_h

pile displacement at depth of z_m (i.e., joint of two segments) (L);

w_L

a fictitious pile displacement at GL projected along the low segment (L);

w_s

w_s (=w_s* p_s/k_s), effective soil movement (L);

w(z), w′(z)

displacement (L) and rotation at depth z;

x

z−z_m, depth measured from z_m (R-E model) (L);

z

depth (L);

z_m

depth of maximum bending moment (L);

α_s

a factor for nonhomogeneous soil movement profile, or on-pile pressure;

β_s

1.08α_s, a factor for quantifying depth of soil deformation (of β_sl_exc);

γ′

effective unit weight of clay or sand (FL⁻³);

η

ω_r/ω_rL, ratio of rotation angle of upper over lower segments;

ν_s

Poisson's ratio of soil;

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

effective overburden stress (FL⁻²);

ϕ′

effective angle of internal friction;

${\varphi }_d^{\mathrm{\prime }}$

angle of dilatancy;

${\varphi }_i^{\mathrm{\prime }}$

effective angle of sliding interface;

ω_r

rotation angle of pile of upper segment (also at ground-level);

ω_rL

rotation angle of lower segment of pile;

ω_s

rotation angle of soil movement profile.

References