Revisiting the Fundamental Concepts of Soil Mechanics Using the General Effective Stress Concept for Saturated Geomaterials

Acknowledgments

Notation

A

long-range interparticle attraction;

b_i

body force due to gravity;

$b_i^{\mathrm{\prime }}$

generalized submerged body force considering buoyancy for saturated geomaterials;

C

compressibility of the porous skeleton;

C_s

compressibility of solid grains;

D

depth of the water above the surface of the deposit;

e

void ratio of geomaterials;

G_s

specific gravity of solid grains;

g_i

acceleration due to gravity;

I_cr

generalized critical hydraulic gradient for various cohesionless geomaterials;

I_j

hydraulic gradient, I_j = ψ_,j/γ_w;

i₀

threshold hydraulic gradient value by Terzaghi (1939);

i_cr

conventional critical hydraulic gradient;

j

“seepage force” to represent the mechanical cause of piping (Terzaghi 1939);

K_ij

permeability tensor for saturated geomaterials;

n

porosity;

R

long-range interparticle repulsion;

u₃

elevation-related gravitational potential of pore fluid;

u_w

pore water/fluid pressure or hydrostatic potential caused by pore fluid pressure;

u_w,j

gradient of pore fluid pressure;

z

ξ₃;

${\beta }_i^{\mathrm{\prime }}$

comprehensive effective body force;

γ_w

unit weight of pore fluid;

γ_wη_i3

generalized buoyancy per unit volume of saturated geomaterial;

γ′

conventional submerged unit weight of soil mass defined by Terzaghi (1943);

γ′′

generalized submerged (effective) unit weight of saturated geomaterials;

δ_ij

Kronecker delta;

δ_3j

component of Kronecker delta δ_ij when i = 3;

η

fraction of pore pressure or effective stress coefficient, η = η₃₃ for the isotropic η_ij;

η_ij

general effective stress coefficient tensor;

η_ijψ_,j

generalized seepage force per unit volume of saturated geomaterial;

λ

dimensionless generalized seepage force;

ξ₃

i = 3rd coordinate of point ξ_i;

ξ_3,dp

elevation of the horizontal datum plane;

ρ_sat

saturated density of the geomaterial;

σ

total stress;

σ_ij

total stress tensor for general geomaterials;

$\overline{\sigma }$

effective normal stress on a horizontal section of submerged sand stratum (Terzaghi 1943);

σ′

effective stress;

${\sigma }_i^{\mathrm{\prime }}$

true intergranular pressure;

${\sigma }_{ij}^{\mathrm{\prime }}$

general effective stress tensor in accordance with η_ij; and

ψ

total seepage potential of pore fluid (water) in the unit of pressure.

References