One-Dimensional Consolidation for Unsaturated Soils under Depth-Dependent Stress Induced by Multistage Load

Data Availability Statement

Notation

C_a

interactive constant with respect to the air phase;

$C_v^a$

consolidation coefficient of volume change with respect to the air phase;

$C_{\sigma }^a$

consolidation coefficient of vertical stress change for the air phase;

C_w

interactive constant with respect to the water phase;

$C_v^w$

consolidation coefficient of volume change with respect to the water phase ;

$C_{\sigma }^w$

consolidation coefficient of vertical stress change for the water phase;

D

differential operator which is equal to ∂/∂z;

g

gravitational acceleration;

H

thickness of soil stratum;

k_a

permeability coefficients of the air phase;

k_w

permeability coefficients of the water phase;

M

molecular mass of air;

$m_1^a$

coefficient of air volume with respect to change in net normal pressure σ − u_a;

$m_1^s$

coefficient of soil skeleton volume with respect to change in net normal pressure σ − u_a;

$m_1^w$

coefficient of water volume with respect to change in net normal pressure σ − u_a;

$m_2^a$

coefficient of air skeleton volume with respect to change in matrix suction u_a − u_w;

$m_2^s$

coefficient of soil skeleton volume with respect to change in matrix suction u_a − u_w;

$m_2^w$

coefficient of water volume with respect to change in matrix suction u_a − u_w;

n

natural number;

n₀

initial porosity;

Q(z, s)

result of the Laplace transform of ∂σ(z, t)/∂t upon time t;

Q′(z, s)

result of first derivative of Q(z, s) with respect to z;

Q_i(z, s)

result of the integration of Q(z, s) against z;

q(t)

vertical load changes with time;

q₀

initial vertical load;

R

universal gas constant;

S_r0

initial degree of saturation;

T

absolute temperature;

t_2n−1

critical time of loading;

u_a

excess pore–air pressure;

$u_a^0$

initial excess pore–air pressure;

${\overline{u}}_a^0$

initial absolute pore–air pressure;

u_w

excess pore–water pressure;

$u_w^0$

initial excess pore–water pressure;

${\tilde{u}}_w^{*}$

particular solution of ${\tilde{u}}_w$;

u_atm

atmospheric pressure;

w

settlement;

$w^{*}$

normalized settlement;

γ_w

unit weight of water;

ɛ_v

total volumetric strain;

σ(z, t)

vertical total stress changes with time and depth;

σ_B

vertical total stress at the bottom surface;

σ_T

vertical total stress at the top surface;

σ_nB

value of final stress at bottom surface by the nth stage loading;

σ_nT

value of final stress at top surface by the nth stage loading; and

λ

characteristic root of differential equation.

References