Cavity Expansion–Contraction-Based Method for Tunnel–Soil–Pile Interaction in a Unified Clay and Sand Model: Drained Analysis

Acknowledgments

Notation

a₀, a

initial and current cavity radius;

e₀

initial void ratio;

e_max, e_min

maximum and minimum void ratio;

G

shear modulus;

K₀

at-rest lateral stress coefficient;

k_i

foundation stiffness;

m

parameter to distinguish spherical and cylindrical scenarios;

N_g

centrifuge scaling factor;

P_a,sph

spherical cavity pressure;

P_load

pile service load;

p′, q

mean and deviatoric stresses;

$p_{0,\mathrm{tip}}^{\mathrm{\prime }}$, ν_0,tip

initial states around the pile tip;

$p_{0,\mathrm{tun}}^{\mathrm{\prime }}$, ν_0,tun

initial states at depth of tunnel center;

Q

pile load capacity;

Q_Vl

pile load capacity after tunnel volume loss;

q_c

cone-tip resistance;

q_t

pile end-bearing capacity;

q_t,Vl

pile end-bearing capacity after tunnel volume loss;

R₀

initial isotropic overconsolidation ratio;

R_Q

reduction factor of pile load capacity;

$R_Q^f$

critical degradation of pile load capacity;

R_Q,SF

critical pile load capacity degradation based on safety factor criterion;

R_Q,s

critical pile load capacity degradation based on pile settlement criterion;

r*, n

spacing ratio and stress-state coefficient;

r_p, b_p

pile radius and pile diameter;

r_t

tunnel radius;

SF₀

initial safety factor;

SF^f

critical safety factor;

SF_Vl

safety factor after tunnel volume loss;

s_pile,Vl

tunneling-induced pile settlement;

V_l,t

tunnel volume loss;

$V_l^{f,\exp }$

critical tunnel volume loss at pile failure based on experimental data;

$V_l^{f,RQ}$

critical tunnel volume loss based on pile-load capacity criterion;

$V_l^{f,SF}$

critical tunnel volume loss based on safety factor criterion;

$V_l^{f,s}$

critical tunnel volume loss based on pile settlement criterion;

V_l,ult

ultimate tunnel volume loss at convergence without support;

x_tp, z_tp

horizontal and vertical distance of tunnel-pile;

z_p

pile depth;

z_t

depth of tunnel center;

Δy

expansion of shear band around pile shaft;

$\mathrm{\Delta }{\sigma }_{rd}^{\mathrm{\prime }}$

additional stress induced by shear band expansion;

δ_f

interface friction angle;

ζ

parameter to unify the expansion and contraction;

κ, μ

elastic constants;

ν

specific volume, = e + 1;

ν₀

initial specific volume, = e₀ + 1;

ξ

state parameter;

${\sigma }_r^{\mathrm{\prime }},{\sigma }_{\theta }^{\mathrm{\prime }}$

radial and tangential stresses;

${\sigma }_{r,s}^{\mathrm{\prime }}$, τ_s

horizontal stress and shaft friction;

ϕ_cs

critical state friction angle; and

ϕ_tx

constant-volume friction angle of conventional triaxial tests.

References