Analytical Study of the Permeability of a Foam-Conditioned Soil

Acknowledgments

Notations

A_s

specific surface (/m);

${\tilde{A}}_S$

dimensionless specific surface;

A_χ

total wetted area of permeation channels;

C_c

curvature coefficient of soil;

C_K

Kozeny constant;

C_u

uniformity coefficient of soil;

d_10,f

effective particle size of foam (m);

d_10,s

effective particle size of soil (m);

FER

foam expansion ratio;

FIR

foam injection ratio;

K_f

permeability of foam (m²);

k

coefficient of permeability of foam-conditioned soil (m/s);

k_ana

calculated coefficient of permeability (m/s);

k_exp

measured coefficient of permeability (m/s);

k_f

coefficient of permeability of foam (m/s);

k_fc

coefficient of permeability in single permeation channel (m/s);

l

sum of the perimeters of all soil particles in the cross section of the conditioned soil (m);

m

number of soil particles in the cross section;

n

porosity of foam-conditioned soil;

n_f

proportion of the water volume in pure foam;

p

number of foam bubbles in the cross section;

p′

number of foam bubbles in contact with soil particles;

q

flow in a single permeation channel (m³/s);

Q

total permeation flow (m³/s);

R

radius of a bubble (m);

R_H

hydraulic radius of the permeation channel (m);

S

cross-sectional area of the conditioned soil (m²);

s

number of effective permeation channels;

s′

number of total permeation channels in pure foam;

s₀

surface area of the volume-equivalent spherical bubble; and

s_f

interfacial area involved in a bubble films contacted with other bubbles;

s_p

surface area presented to liquid flow of a bubble;

s_t

total surface area of a bubble;

U

dimensionless excess energy density;

u

average flow velocity of the fluid in single permeation channel (m/s);

V_f

volume of the foam (m³);

V_l

volume of the solution (m³);

V_p

total volume of the pores in a material;

v

apparent permeation velocity in the foam-conditioned soil (m/s);

W

cross-sectional area of the permeation channel (m²);

β

fineness of foam relative to the particles of soil;

γ

unit weight of fluid (kN/m³);

μ

dynamic viscosity of the fluid (Pa · s); and

χ

wetted perimeter of the permeation channel (m).

References