Settlement and Stress Analysis of Soil–Cement Column-Reinforced Foundation under an In Situ Stabilized Layer

Acknowledgments

Notation

d_c

diameter of columns (m);

d_e

effective diameter of the unit cell (m);

E_c

elastic modulus of the column materials (kN/m²);

E_oed,s

oedometer modulus of the soil (kN/m²);

E_s

elastic modulus of the soil (kN/m²);

f

friction between the inner cylinder and the outer cylinder in the embankment (kN/m²);

f_L

friction force between the inner and the outer columns of the stabilized soil layer (kN/m²);

G_s

shear modulus of the soil (kN/m²);

H_e

height of the embankment fill (m);

h_e

the height of equal settlement plane (m);

K_s0

coefficient of at-rest pressure (dimensionless);

L_c

length of the columns (m);

L_L

depth of the solidification (m);

m

area replacement ratio (dimensionless);

p_cL

vertical stress of the inner cylinder in the stabilized soil (kN/m²);

q_c

stress acting on the surface of the column (kN/m²);

q_cL

vertical stress applied at the surface of the stabilized layer above the column (kN/m²);

q_i

vertical stress of the embankment fill above the column (kN/m²);

q_o

vertical stress of the embankment fill above the soil (kN/m²);

q_s

stress acting on the surface of the soft soil (kN/m²);

q_sL

vertical stress applied at the surface of the stabilized layer above the soil (kN/m²);

r_c

radius of columns (m);

S

spacing of columns (m);

S_c

settlement at the surface of the column (m);

S_cL

settlement at the surface of the stabilized layer above the column (m);

S_s

settlement at the surface of the foundation soil (m);

v_c

Poisson's ratio of columns (dimensionless);

v_s

Poisson's ratio of the soil (dimensionless);

w_cz

vertical settlement of the column element at a depth z (m);

w_d

differential settlement at the bottom of the stabilized soil layer (m);

w_de

differential settlement at the bottom of the embankment fill (m);

w_rz

vertical settlement of the soil element at the coordinate (r, z) (m);

w_sN

vertical settlement of the Nth soil element (m);

α_cz, β_c

vertical settlement parameters;

γ_e

unit weight of the embankment soil (kN/m³);

γ_L

unit weight of the stabilized soil layer (kN/m³);

γ_s

unit weight of the foundation soil (kN/m³);

γ_s

unit weight of the soil (kN/m³);

Δσ_rc

radial stress increment of the columns (kPa);

Δσ_zc

vertical stress increment of the columns (kPa);

Δσ_zs

vertical stress increment of the surrounding soil (kPa);

δ_c

radial displacement of the column (m);

ɛ_rc

radial strain of the columns (dimensionless);

ɛ_zc

vertical strain of the columns (dimensionless);

σ_rs

confining stress from the surrounding soil (kN/m²);

σ_sN,j, σ_sN,j+1

vertical stresses acting on the top and bottom of the (N, j)th soil element (kN/m²);

τ_rz

shear stress (kN/m²);

φ_e

angle of shearing resistance of the embankment soil (°); and

φ_L

angle of shearing resistance of the stabilized layer (°).

References