Effect of Preloading with Consolidation on the Undrained Bearing Capacity of Ring Foundations

Acknowledgments

Notation

c_v

coefficient of consolidation;

e_c

void ratio in the consolidated state;

e₀

void ratio in the initial state;

e₁

void ratio at p′ = 1 kPa;

f

curve-fitting coefficient;

G_f

relative gain in undrained capacity for full primary consolidation (q_cu,f/q_uu);

G_p

relative gain in undrained capacity for partial consolidation [(q_cu,p − q_uu)/(q_cu,f − q_uu)];

G_s

specific gravity;

$K_0^{nc}$

coefficient of earth pressure at rest for NC clays;

$K_0^{oc}$

coefficient of earth pressure at rest for OC clays;

k

permeability;

M_cs

stress ratio in the critical state;

m_g, m_s

coefficients defining a power in fitting curves;

N_c

undrained bearing capacity factor (q_uu/s_u0);

OCR

overconsolidation ratio;

$p_c^{\mathrm{\prime }}$

preconsolidation pressure;

$p_0^{\mathrm{\prime }}$

initial mean effective stress;

p

preload ratio (σ_p/q_uu);

Q

vertical compressive force;

Q_u

undrained bearing capacity;

q

vertical compressive stress;

q_cu

consolidated undrained bearing capacity;

q_cu,f

consolidated undrained bearing capacity after full consolidation;

q_cu,p

consolidated undrained bearing capacity after partial consolidation;

q_u

unit undrained bearing capacity;

q_uu

unconsolidated undrained bearing capacity;

R_i

inside radius;

R₀

outside radius;

R²

coefficient of determination;

s_u

undrained shear strength;

s_uc

undrained shear strength in the consolidated state;

s_ui

undrained shear strength in the initial condition;

s_u0

undrained shear strength at the ground surface;

T

time factor [c_vt/(2R₀)²];

T_50,g

time factor [c_vt/(2R₀)²] required for half the maximum potential gain;

T_50,s

time factor [c_vt/(2R₀)²] required for half the consolidation settlement;

t

consolidation time;

t₀

consolidation time at U = 0.0;

t₉₉

consolidation time at U = 0.99;

U

degree of consolidation (w_c/w_cf);

w_c

consolidation settlement measured at (R_i + R₀)/2;

w_cf

final consolidation settlement measured at (R_i + R₀)/2;

z

depth;

γ_sat

saturated bulk unit weight;

γ_w

unit weight of water;

Δu

excess pore-water pressure;

θ

Lode angle;

κ

recompression index;

λ

virgin compression index;

μ

Poisson’s ratio;

ρ

gradient of shear strength increasing with depth;

σ_p

preloading;

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

vertical effective stress; and

${\phi }_{cs}^{\mathrm{\prime }}$

critical state friction angle.

References