Finite Hankel Transform Method–Based Analysis of Axisymmetric Free-Strain Consolidation Theory for Unsaturated Soils

Data Availability Statement

Acknowledgments

Notation

C_w, C_a

relevant water and air interaction coefficients (−);

$C_{vr}^w,C_{vr}^a$

radial water and air coefficients of volume change (−);

$C_{vz}^w,C_{vz}^a$

vertical water and air coefficients of volume change (−);

$C_q^w,C_q^a$

load-related water and air interaction coefficients (−);

g

gravitational acceleration (∼9.807 m · s⁻²);

$h_0,h$

thickness of the sand cushion and unsaturated soil layer (m);

k_ar, k_az

radial and vertical air permeability coefficients in the influence area (m/s);

$k_{ar}^s,k_{wr}^s$

radial permeability coefficients of air and water in the smear zone (m/s);

k_at, k_wt

air and water permeability coefficients of the sand cushion (m/s);

k_wr, k_wz

radial and vertical water permeability coefficients in the influence area (m/s);

M

molecular mass of air (approximately 28.966 kg · kmol⁻¹);

$m_1^w,m_1^a$

coefficient of water and air volume changing with an increase in net normal stress (σ_z − u_a) (kPa⁻¹);

$m_2^w,m_2^a$

coefficient of water and air volume changing with an increase in matric suction (u_a − u_w) (kPa⁻¹);

n₀, S_r0

initial porosity and degree of saturation (−);

R

molar air constant (approximately 8.314 J · mol⁻¹ · K⁻¹);

$R_{vz}^w,R_{vz}^a$

vertical semipermeability factors of water and air (−);

$R_{vr}^w,R_{vr}^a$

radial semipermeability factors of water and air (−);

r_d, r_s, r_e

radius of a vertical well, smear zone, and influence zone (m).

T

absolute temperature (=t₀ + 273 K);

u_atm

atmospheric pressure (approximately 101.3 kPa);

u_w, u_a

excess pore pressures of water and air phases (kPa);

$u_w^0,u_a^0$

initial excess pore-water and pore-air pressures (kPa); and

γ_w

unit weight of water (approximately 9.8 kN · m⁻³).

References