3D Numerical Analysis of a Single Footing on Soft Soil Reinforced by Rigid Inclusions

Acknowledgments

Notation

A

inclusion cross-sectional area (m²);

B

side length of the concrete square footing (m);

c'

effective cohesion (kN/m²);

d

diameter of circular inclusion (m);

E

Young’s modulus (MPa);

E_i

average load efficiency for a single inclusion (%);

E_L

average load efficiency for all inclusions (%);

E_m

pressuremeter (Menard) modulus in pressuremeter tests (MPa);

E_s

settlement efficiency;

e

horizontal distance between the eccentric loading center and the footing center (m);

e/B

eccentricity ratio;

G

shear modulus;

H

thickness of the load transfer platform (m);

K₀

earth pressure coefficient;

K_{0_NC}

earth pressure coefficient at rest;

r

the radius of circular inclusion (m);

I_y and I_z

second moment of area of the inclusion’s cross section along y- and z-directions;

M

critical state ratio;

M_fy/M_fz

inclusion bending moment in the y/z-direction (kN · m);

N

axial load of the inclusion cross section (kN);

p_c0

preconsolidation pressure (kPa);

p_L

limit pressure in pressuremeter tests (MPa);

p′

mean effective stress (kPa);

Q

total load applied on the footing (kN);

Q_p

load transmitted to one inclusion (kN);

Q_{p_L}/_{_R}

load transmitted to the left/right side inclusion (kN);

q_c

static cone penetration resistance (MPa);

s

inclusion center-to-center spacing (for inclusions on a square grid) (m);

u

footing center settlement with reinforcement (mm);

u_un

footing center settlement without reinforcement (mm);

v

specific volume;

W

sum of the footing weight and the LTP layer weight;

x/y/z

coordinate system directions for inclusions;

α

rheological coefficient of soil;

σ_xx

axial normal stress of inclusion (kPa);

γ

soil unit weight (kN/m³);

ν

Poisson ratio;

v_λ

value of the specific volume for p′—1 kPa (the reference pressure) on the critical state line;

φ′

internal friction angle (°);

ψ

dilation angle (°);

λ

isotropic virgin consolidation line index; and

κ

isotropic swelling line index.

References