Density-Dependent Model of Soil–Water Characteristic Curves and Application in Predicting Unsaturated Soil–Structure Bearing Resistance

Acknowledgments

Notation

a, m, n

fitting parameters (dimensionless);

A_i

circular cross-section area of a cylindrical capillary tube (m²);

A_b

cross-sectional area of the pile base (m²);

b_γ, b_q, b_c

base inclination factors (dimensionless);

B

equivalent width of footing (m);

cos α

wetting coefficient (dimensionless);

c′

effective cohesion (Pa);

C_i

perimeter of pile section i (m);

D

disturbance function (dimensionless);

d

embedment depth of footing (m);

d_γ, d_q, d_c

embedment depth factors (dimensionless);

e

void ratio (dimensionless);

e₀

initial void ratio at reference state (dimensionless);

e_i

arbitrary initial void ratio (dimensionless);

g_γ, g_q, g_c

ground inclination factors (dimensionless);

h_i

total pore length of a capillary tube (m);

i_γ, i_q, i_c

load inclination factors (dimensionless);

K

static earth pressure coefficient (dimensionless);

L_i

length of pile section i (m);

m_si

solid mass corresponds to segment i (kg);

N

number of measured data pairs for the same degree of saturation (dimensionless);

N_γ, N_q, N_c

bearing capacity factors (dimensionless);

n

soil porosity (dimensionless);

n_i

number of spherical soil particles (dimensionless);

$(n_i{)}_{e_0}$

number of soil particles corresponding to reference initial void ratio (dimensionless);

$(n_i{)}_{e_i}$

number of soil particles corresponding to arbitrary initial void ratio (dimensionless);

OCR

over-consolidation ratio (dimensionless);

q

surcharge at the base of the footing (Pa);

q_u

ultimate bearing capacity (Pa);

Q_b

end-bearing resistance (N);

Q_f

skin resistance (N);

Q_ult

ultimate bearing capacity (N);

R_i

mean particle radius (m);

R_i0

mean particle radius at reference state (m);

R_ii

mean particle radius at arbitrary state (m);

r_i

mean pore radius (m);

S

degree of saturation (dimensionless);

$S_{e_0}$

degree of saturation corresponding to reference SWCC (dimensionless);

S_p

predicted degree of saturation (dimensionless);

S_m

measured degree of saturation (dimensionless);

S_r

residual saturation degree (dimensionless);

s_γ, s_q, s_c

shape factors (dimensionless);

u_a

air–pore pressure (Pa);

u_w

water–pore pressure (Pa);

V

total volume of a soil sample (m³);

V_s

total solid volume of a soil sample (m³);

V_si

volume of a spherical soil particle (m³);

V_v

total void volume per unit sample mass (m³);

V_vi

void volume corresponding to segment i (m³);

W_p

weight of the pile (N);

α

air–water contact angle (degree);

β_i

resistance factor (dimensionless);

χ

Bishop’s parameter (dimensionless);

δ

calibrated factor considering actual particle size and shape (dimensionless);

γ

unit weight of the overburden material (N/m³);

λ

calibrated parameter (dimensionless);

φ′

internal friction angle (degree);

φ_i

interfacial effective friction angle (degree);

ρ

dry density of soil (kg/m³);

ρ_s

particle density (kg/m³);

θ

volumetric water content (dimensionless);

σ_s

surface tension (N/m);

σ

total stress (Pa);

τ

unsaturated shear strength (Pa);

ν

specific volume (dimensionless);

ψ

matric suction (Pa);

ψ_r

residual matric suction (Pa);

${\psi }_{e_0}$

matric suction corresponding to reference initial void ratio (Pa); and

${\psi }_{e_i}$

matric suction corresponding to arbitrary initial void ratio (Pa).

References