Analytical Solutions for Consolidation of Unsaturated Soil with Time-Dependent Boundary Conditions

Acknowledgments

Notation

C_a

interactive constant associated with the air phase;

C_w

interactive constant associated with the water phase;

$C_v^a$

coefficient of volume change with respect to the air phase;

$C_v^w$

coefficient of volume change with respect to the water phase;

$c_{\sigma }^a$

consolidation parameter with respect to the air phase;

$c_{\sigma }^w$

consolidation parameter with respect to the water phase;

g

acceleration due to gravity;

H

thickness of the soil layer;

k_a

coefficient of air permeability, obtained by the permeability test;

k_w

coefficient of water permeability, obtained by the permeability test;

M

molecular mass of air;

$m_{1k}^a$

coefficient of air volume change caused by the change of the net-normal stress, obtained by triaxial test, determined as the slope of the (σ − u_a) plot when d(u_a − u_w) is zero;

$m_2^a$

coefficient of air volume change caused by the change of unit matric suction, obtained by triaxial test, determined as the slope of the (u_a − u_w) plot when d(σ − u_a) is zero;

$m_{1k}^w$

coefficient of water volume change caused by the change of net-normal stress, obtained by triaxial test, determined as the slope of the (σ − u_a) plot when d(u_a − u_w) is zero;

$m_2^w$

coefficient of water volume change caused by the change of unit matric suction, obtained by triaxial test, determined as the slope of the (u_a − u_w) plot when d(σ − u_a) is zero;

n

porosity of the soil before loading, obtained by the porosity test;

q(t)

external time-dependent load applied on the top surface of the soil;

R

universal gas constant;

S

degree of saturation;

T

absolute temperature;

T_k(t)

corresponding function of time;

t

elapsed time;

u

excess pore pressure vector;

u_a

excess pore-air pressure;

${\overline{u}}_a$

absolute pore-air pressure;

${\overline{u}}_{\mathrm{atm}}$

atmospheric pressure;

u^d

function specified to satisfy the homogeneous boundary conditions;

u^s

function specified to satisfy the time-dependent boundary conditions;

u_w

excess pore-water pressure;

x

investigated depth;

${\mathit{X}}_k^d$

kth eigenfunction;

γ_w

unit weight of water; and

ω_k

kth positive root of the characteristic equation.

References