Analytical Solutions for Radial Consolidation of Soft Ground Improved by Composite Piles Considering Time and Depth-Dependent Well Resistance

Acknowledgments

Notation

A_c

cross-sectional area of composite pile (m²);

A_e

cross-sectional area of entire unit cell (m²);

A_g

cross-sectional area of gravel shell (m²);

A_p

cross-sectional area of impervious core (m²);

B₁

factor of initial clogging (dimensionless);

B₂

factor of depth-dependent well resistance (dimensionless);

B₃

factor of time-dependent clogging (/s);

b_c

width of rectangular composite pile (m);

b_p

width of rectangular core (m);

E_com

area-weighted constrained composite compression modulus (Pa);

E_g

constrained compression modulus of granular shell (Pa);

E_p

constrained compression modulus of impervious core (Pa);

E_s

constrained compression modulus of surrounding soil (Pa);

e

the base of irrational number (dimensionless);

F_c

parameter to reflect disturbance effect caused by construction of composite columns (dimensionless);

$F_i(\overline{Z})$

function of Bessel function and Neumann function (dimensionless);

f(t)

function of time-dependent clogging (dimensionless);

g(z)

function of depth-dependent well resistance (dimensionless);

H

thickness of soft soil as well as length of composite pile (m);

h(r)

function of radial distance (dimensionless);

$J_i(\overline{Z})$

ith Bessel function (dimensionless);

k_g

permeability coefficient of vertical drain at any time (m/s);

k_g0

permeability coefficient of vertical drain at initial moment (m/s);

k_h

horizontal permeability coefficient of undisturbed soil (m/s);

k_r(r)

horizontal permeability coefficient of soil (m/s);

k_s

permeability coefficient at interface of gravel shell and soil (m/s);

l_c

length of rectangular composite pile (m);

l_p

length of rectangular core (m);

$N_i(\overline{Z})$

ith Neumann function (dimensionless);

p(t)

surcharge loading (Pa);

p₀

surcharge loading at initial time (Pa);

r

horizontal distance from any position to center of pile (m);

r_c

equivalent radius of composite pile (m);

r_ci

initial radius of composite pile (m);

r_e

equivalent outer radius of unit cell (m);

r_o

radius of hole (m);

r_p

equivalent radius of impervious core (m);

r_pi

initial radius of impervious core (m);

r_s

radius of disturbed soil zone (m);

s_c

center-to-center spacing of composite piles (m);

s_t

settlement of composite ground at any time (m);

s_∞

final settlement of composite ground (m);

T_h

horizontal time factor of soil (dimensionless);

t

elapsed time (s);

U(t)

total average degree of radial consolidation of composite ground (dimensionless);

U_r $(\overline{Z},t)$

radial average degree of consolidation at any depth (dimensionless);

${\overline{u}}_g$

excess pore water pressure within gravel shell at a particular depth, ${\overline{u}}_g$ = ${\overline{u}}_g$(z, t) (Pa);

u_s

excess pore water pressure in soil at any time and at any point, u_s = u_s(r, z, t) (Pa);

$\overline{u}(z,t)$

averaged excess pore water pressure at particular depth for entire composite ground (Pa);

${\overline{u}}_s$

averaged excess pore water pressure within soil at particular depth, ${\overline{u}}_s={\overline{u}}_s(z,t)$ (Pa);

W_m

series of parameters (dimensionless);

z

vertical distance from any position to composite ground surface (m);

α_c

ratio of area replacement ratio of composite pile (dimensionless);

α_p

ratio of cross-sectional area of impervious core to composite pile (dimensionless);

α₃

time-dependent clogging factor (dimensionless);

γ_w

unit weight of water (N/m³);

ɛ_z

vertical strain (dimensionless);

η_m

series of parameters (m);

λ_m

series of parameters (dimensionless);

${\overline{\sigma }}_g$

average stress of gravel shell (Pa);

${\overline{\sigma }}_p$

average stress of impervious core (Pa); and

${\overline{\sigma }}_s$

average stress of surrounding soil (Pa).

References