Large-Strain Radial Consolidation Analysis Incorporating Soil Smear and Well Resistance Effect

Data Availability Statement

Notation

A

total area of the influence zone of the drain;

A_s

area of smear zone;

A_u

area of undisturbed zone;

a

Lagrangian coordinate;

a_c

compressibility ratio;

b

function of r;

b_s

ratio of area of smear zone to the total area of influence zone;

C_c

compression index;

C_hi

initial coefficient of radial consolidation;

C_k

permeability index;

C_r

recompression index;

EPWP

excess pore-water pressure;

e

average void ratio at any time t and depth z;

e₀

average initial void ratio at any depth z;

FDM

finite difference method;

f(r)

function of radial distance r;

f_j

value of function f(r) at the jth node of radial distance;

g(r)

function of radial distance r;

g_j

value of function g(r) at the jth node of radial distance;

i_h

hydraulic gradient in the horizontal direction;

$\tilde{k}$

permeability at any time t and depth z for non-Darcian flow;

$\overline{\tilde{k}}$

average permeability at any time t and depth z;

${\overline{\tilde{k}}}_0$

average initial permeability at any depth z;

${\tilde{k}}_0$

initial permeability at any depth z for non-Darcian flow;

${\tilde{k}}_h$

permeability soil in horizontal direction for non-Darcian flow;

${\tilde{k}}_{hs}$

horizontal permeability in smear zone at a radial distance r from the center of the drain;

${\tilde{k}}_s$

horizontal permeability in smear zone at the soil–drain interface under non-Darcian flow;

${\tilde{k}}_u$

horizontal permeability in the undisturbed zone under non-Darcian flow;

${\tilde{k}}_{u0}$

initial horizontal permeability in the undisturbed zone under non-Darcian flow;

L

initial height of the soil deposit;

m_vs

volume compressibility in the smear zone at the soil–drain interface;

m_vu

volume compressibility in the undisturbed zone;

m_vu0

initial volume compressibility in the undisturbed zone;

μ

ratio of constant B to A;

N

constant, function of r_e, r_w, q_w, and θ;

n

non-Darcian parameter;

Q

surcharge load on the soil deposit;

Q_in(t)

total flow entering the drain from the surrounding soil at any time t;

q_w

discharge capacity of the drain;

$\overline{q^{\mathrm{\prime }}}$

total stress at any time t and depth z in the soil sample;

r

radial distance measured from the center of the drain;

r_e

radius of influence zone measured from the center of the drain;

r_j

radial distance of the jth node from the center of the drain;

r_s

radius of smear zone measured from the center of the drain;

r_w

equivalent radius of the vertical drain;

S

ratio of radius of smear zone to the radius of drain;

S(t)

settlement of soil deposit at any time t;

S_f

final settlement of the soil deposit;

T_hu

time factor;

${\overline{U}}_p$

average degree of consolidation at any time t based on EPWP dissipation;

${\overline{U}}_s$

average degree of consolidation at any time t based on settlement of the soil deposit;

u

EPWP at a radial distance r;

$u_{s_j}$

EPWP in the smear zone at the jth node of the radial distance;

$u_{s_{j+1}}$

EPWP in the smear zone at the (j + 1)th node of the radial distance;

$u_{u_j}$

EPWP in the undisturbed zone at the jth node of the radial distance;

$u_{u_{j+1}}$

EPWP in the undisturbed zone at the (j + 1)th node of the radial distance;

u_i,j

EPWP corresponding to the ith node of the radial distance grid and the jth node of the time grid;

u_i+1,j

EPWP corresponding to the (i + 1)th node of the radial distance grid and the jth node of the time grid;

u_s

EPWP in the smear zone at any radial distance r and time t;

u_u

EPWP in the undisturbed zone at any radial distance r and time t;

${\overline{u}}_{r_j}$

average EPWP at the jth node of the time grid;

${\overline{u}}_{r_{j+1}}$

average EPWP at the (j + 1)th node of the time grid;

${\overline{u}}_{r_{j-1}}$

average EPWP at the (j − 1)th node of the time grid;

${\overline{u}}_r$

radial average of EPWP over the entire influence zone at any depth z and time t;

${\overline{u}}_s$

average EPWP in the smear zone;

${\overline{u}}_u$

average EPWP in the undisturbed zone;

${\overline{u}}_w$

average EPWP at the soil–drain interface in the smear zone;

v_r(r)

radial flow velocity at any radial distance r from the center of the drain and time t;

x_j

function of f_j, g_j, and β(t);

Y_i

function of f_i and g_i;

β(t)

function of time;

Δr

small interval of radial distance;

Δt

small interval of time;

φ

constant obtained while determining the radial average of EPWP;

γ_w

unit weight of water;

κ

permeability ratio;

λ

constant, function of the compressibility ratio;

θ

constant, function of λ and b_s;

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

radial average of effective stress over the entire influence zone at any time t and depth z;

$\overline{{\sigma }_0^{\mathrm{\prime }}}$

radial average initial effective stress over the entire influence zone at any depth z;

$\overline{{\sigma }_p^{\mathrm{\prime }}}$

average preconsolidation pressure for the entire influence zone;

$\overline{{\sigma }_{ps}^{\mathrm{\prime }}}$

average preconsolidation pressure for the smear zone;

$\overline{{\sigma }_{pu}^{\mathrm{\prime }}}$

average preconsolidation pressure for the undisturbed zone;

$\overline{{\sigma }_s^{\mathrm{\prime }}}$

average effective stress in the smear zone;

$\overline{{\sigma }_{s0}^{\mathrm{\prime }}}$

initial average effective stress in the smear zone;

$\overline{{\sigma }_u^{\mathrm{\prime }}}$

average effective stress in the undisturbed zone;

$\overline{{\sigma }_{u0}^{\mathrm{\prime }}}$

initial average effective stress in the undisturbed zone;

ω

constant;

ξ

convective coordinate;

ξ_0(t)

height of the sample at any time t in the convective coordinate;

ζ

constant, function of m_vu, ${\tilde{k}}_u$, and θ; and

ζ₀

constant, a function of m_vu0, ${\tilde{k}}_{u0}$, and θ.

References